Simple Linear Equations: In Class 8, students learn to solve linear equations in one variable. This blog post covers all exercises from Chapter 4, offering step-by-step solutions. Additionally, we’ve included 54 extra practice questions with solutions to help you master solving linear equations effectively.
Questions of Maths Simple Linear Equations
Exercise 4.1
- Solve the equation:3x+2=113x + 2 = 113x+2=11Solution:Step 1: Subtract 2 from both sides:3x=11−23x = 11 – 23x=11−2 3x=93x = 93x=9Step 2: Divide both sides by 3:x=93=3x = \frac{9}{3} = 3x=39=3Answer: x=3x = 3x=3
- Solve the equation:5x−7=3x+15x – 7 = 3x + 15x−7=3x+1Solution:Step 1: Subtract 3x3x3x from both sides:5x−3x−7=3x−3x+15x – 3x – 7 = 3x – 3x + 15x−3x−7=3x−3x+1 2x−7=12x – 7 = 12x−7=1Step 2: Add 7 to both sides:2x=1+72x = 1 + 72x=1+7 2x=82x = 82x=8Step 3: Divide both sides by 2:x=82=4x = \frac{8}{2} = 4x=28=4Answer: x=4x = 4x=4
Exercise 4.2
- Solve the equation:7x+2=3x+107x + 2 = 3x + 107x+2=3x+10Solution:Step 1: Subtract 3x3x3x from both sides:7x−3x+2=3x−3x+107x – 3x + 2 = 3x – 3x + 107x−3x+2=3x−3x+10 4x+2=104x + 2 = 104x+2=10Step 2: Subtract 2 from both sides:4x=10−24x = 10 – 24x=10−2 4x=84x = 84x=8Step 3: Divide both sides by 4:x=84=2x = \frac{8}{4} = 2x=48=2Answer: x=2x = 2x=2
- Solve the equation:4x−7=2x+34x – 7 = 2x + 34x−7=2x+3Solution:Step 1: Subtract 2x2x2x from both sides:4x−2x−7=2x−2x+34x – 2x – 7 = 2x – 2x + 34x−2x−7=2x−2x+3 2x−7=32x – 7 = 32x−7=3Step 2: Add 7 to both sides:2x=3+72x = 3 + 72x=3+7 2x=102x = 102x=10Step 3: Divide both sides by 2:x=102=5x = \frac{10}{2} = 5x=210=5Answer: x=5x = 5x=5
Exercise 4.3
- Solve the equation:x2−3=4\frac{x}{2} – 3 = 42x−3=4Solution:Step 1: Add 3 to both sides:x2=4+3\frac{x}{2} = 4 + 32x=4+3 x2=7\frac{x}{2} = 72x=7Step 2: Multiply both sides by 2:x=7×2=14x = 7 \times 2 = 14x=7×2=14Answer: x=14x = 14x=14
- Solve the equation:2x+3=5x−62x + 3 = 5x – 62x+3=5x−6Solution:Step 1: Subtract 2x2x2x from both sides:2x−2x+3=5x−2x−62x – 2x + 3 = 5x – 2x – 62x−2x+3=5x−2x−6 3=3x−63 = 3x – 63=3x−6Step 2: Add 6 to both sides:3+6=3x−6+63 + 6 = 3x – 6 + 63+6=3x−6+6 9=3×9 = 3×9=3xStep 3: Divide both sides by 3:x=93=3x = \frac{9}{3} = 3x=39=3Answer: x=3x = 3x=3
Exercise 4.4
- Solve the equation:5x−7=3x+95x – 7 = 3x + 95x−7=3x+9Solution:Step 1: Subtract 3x3x3x from both sides:5x−3x−7=3x−3x+95x – 3x – 7 = 3x – 3x + 95x−3x−7=3x−3x+9 2x−7=92x – 7 = 92x−7=9Step 2: Add 7 to both sides:2x=9+72x = 9 + 72x=9+7 2x=162x = 162x=16Step 3: Divide both sides by 2:x=162=8x = \frac{16}{2} = 8x=216=8Answer: x=8x = 8x=8
- Solve the equation:4x+6=2x+104x + 6 = 2x + 104x+6=2x+10Solution:Step 1: Subtract 2x2x2x from both sides:4x−2x+6=2x−2x+104x – 2x + 6 = 2x – 2x + 104x−2x+6=2x−2x+10 2x+6=102x + 6 = 102x+6=10Step 2: Subtract 6 from both sides:2x=10−62x = 10 – 62x=10−6 2x=42x = 42x=4Step 3: Divide both sides by 2:x=42=2x = \frac{4}{2} = 2x=24=2Answer: x=2x = 2x=2
Additional 40 Questions with Solutions
Let me now add 40 additional problems with solutions.
Q1. Solve the equation:
3x+5=113x + 5 = 113x+5=11
Solution:3x=11−5⇒3x=6⇒x=63=23x = 11 – 5 \quad \Rightarrow \quad 3x = 6 \quad \Rightarrow \quad x = \frac{6}{3} = 23x=11−5⇒3x=6⇒x=36=2
Q2. Solve the equation:
2x−7=3x+22x – 7 = 3x + 22x−7=3x+2
Solution:2x−3x=2+7⇒−x=9⇒x=−92x – 3x = 2 + 7 \quad \Rightarrow \quad -x = 9 \quad \Rightarrow \quad x = -92x−3x=2+7⇒−x=9⇒x=−9
Q3. Solve the equation:
4x+6=2x+104x + 6 = 2x + 104x+6=2x+10
Solution:4x−2x=10−6⇒2x=4⇒x=42=24x – 2x = 10 – 6 \quad \Rightarrow \quad 2x = 4 \quad \Rightarrow \quad x = \frac{4}{2} = 24x−2x=10−6⇒2x=4⇒x=24=2
Q4. Solve the equation:
5x+9=2x+185x + 9 = 2x + 185x+9=2x+18
Solution:5x−2x=18−9⇒3x=9⇒x=93=35x – 2x = 18 – 9 \quad \Rightarrow \quad 3x = 9 \quad \Rightarrow \quad x = \frac{9}{3} = 35x−2x=18−9⇒3x=9⇒x=39=3
Q5 – Q40
Q5. Solve the equation:
6x+4=3x+166x + 4 = 3x + 166x+4=3x+16
Solution:6x−3x=16−4⇒3x=12⇒x=123=46x – 3x = 16 – 4 \quad \Rightarrow \quad 3x = 12 \quad \Rightarrow \quad x = \frac{12}{3} = 46x−3x=16−4⇒3x=12⇒x=312=4
Q6. Solve the equation:
7x−3=4x+97x – 3 = 4x + 97x−3=4x+9
Solution:7x−4x=9+3⇒3x=12⇒x=123=47x – 4x = 9 + 3 \quad \Rightarrow \quad 3x = 12 \quad \Rightarrow \quad x = \frac{12}{3} = 47x−4x=9+3⇒3x=12⇒x=312=4
Q7. Solve the equation:
8x+5=2x+298x + 5 = 2x + 298x+5=2x+29
Solution:8x−2x=29−5⇒6x=24⇒x=246=48x – 2x = 29 – 5 \quad \Rightarrow \quad 6x = 24 \quad \Rightarrow \quad x = \frac{24}{6} = 48x−2x=29−5⇒6x=24⇒x=624=4
Q8. Solve the equation:
3x+7=2x+103x + 7 = 2x + 103x+7=2x+10
Solution:3x−2x=10−7⇒x=33x – 2x = 10 – 7 \quad \Rightarrow \quad x = 33x−2x=10−7⇒x=3
Q9. Solve the equation:
5x−6=3x+85x – 6 = 3x + 85x−6=3x+8
Solution:5x−3x=8+6⇒2x=14⇒x=142=75x – 3x = 8 + 6 \quad \Rightarrow \quad 2x = 14 \quad \Rightarrow \quad x = \frac{14}{2} = 75x−3x=8+6⇒2x=14⇒x=214=7
Q10. Solve the equation:
2x+8=122x + 8 = 122x+8=12
Solution:2x=12−8⇒2x=4⇒x=42=22x = 12 – 8 \quad \Rightarrow \quad 2x = 4 \quad \Rightarrow \quad x = \frac{4}{2} = 22x=12−8⇒2x=4⇒x=24=2
Q11. Solve the equation:
9x−4=2x+239x – 4 = 2x + 239x−4=2x+23
Solution:9x−2x=23+4⇒7x=27⇒x=2779x – 2x = 23 + 4 \quad \Rightarrow \quad 7x = 27 \quad \Rightarrow \quad x = \frac{27}{7}9x−2x=23+4⇒7x=27⇒x=727
Q12. Solve the equation:
5x+3=2x+185x + 3 = 2x + 185x+3=2x+18
Solution:5x−2x=18−3⇒3x=15⇒x=153=55x – 2x = 18 – 3 \quad \Rightarrow \quad 3x = 15 \quad \Rightarrow \quad x = \frac{15}{3} = 55x−2x=18−3⇒3x=15⇒x=315=5
Q13. Solve the equation:
7x−9=5x+37x – 9 = 5x + 37x−9=5x+3
Solution:7x−5x=3+9⇒2x=12⇒x=122=67x – 5x = 3 + 9 \quad \Rightarrow \quad 2x = 12 \quad \Rightarrow \quad x = \frac{12}{2} = 67x−5x=3+9⇒2x=12⇒x=212=6
Q14. Solve the equation:
3x−5=2x+43x – 5 = 2x + 43x−5=2x+4
Solution:3x−2x=4+5⇒x=93x – 2x = 4 + 5 \quad \Rightarrow \quad x = 93x−2x=4+5⇒x=9
Q15. Solve the equation:
2x+5=112x + 5 = 112x+5=11
Solution:2x=11−5⇒2x=6⇒x=62=32x = 11 – 5 \quad \Rightarrow \quad 2x = 6 \quad \Rightarrow \quad x = \frac{6}{2} = 32x=11−5⇒2x=6⇒x=26=3
Q16. Solve the equation:
3x+4=2x+103x + 4 = 2x + 103x+4=2x+10
Solution:3x−2x=10−4⇒x=63x – 2x = 10 – 4 \quad \Rightarrow \quad x = 63x−2x=10−4⇒x=6
Q17. Solve the equation:
4x−7=5x+84x – 7 = 5x + 84x−7=5x+8
Solution:4x−5x=8+7⇒−x=15⇒x=−154x – 5x = 8 + 7 \quad \Rightarrow \quad -x = 15 \quad \Rightarrow \quad x = -154x−5x=8+7⇒−x=15⇒x=−15
Q18. Solve the equation:
6x+2=3x+86x + 2 = 3x + 86x+2=3x+8
Solution:6x−3x=8−2⇒3x=6⇒x=63=26x – 3x = 8 – 2 \quad \Rightarrow \quad 3x = 6 \quad \Rightarrow \quad x = \frac{6}{3} = 26x−3x=8−2⇒3x=6⇒x=36=2
Q19. Solve the equation:
5x+3=2x+185x + 3 = 2x + 185x+3=2x+18
Solution:5x−2x=18−3⇒3x=15⇒x=153=55x – 2x = 18 – 3 \quad \Rightarrow \quad 3x = 15 \quad \Rightarrow \quad x = \frac{15}{3} = 55x−2x=18−3⇒3x=15⇒x=315=5
Q20. Solve the equation:
7x−3=2x+127x – 3 = 2x + 127x−3=2x+12
Solution:7x−2x=12+3⇒5x=15⇒x=155=37x – 2x = 12 + 3 \quad \Rightarrow \quad 5x = 15 \quad \Rightarrow \quad x = \frac{15}{5} = 37x−2x=12+3⇒5x=15⇒x=515=3
Q21. Solve the equation:
6x−4=2x+126x – 4 = 2x + 126x−4=2x+12
Solution:6x−2x=12+4⇒4x=16⇒x=164=46x – 2x = 12 + 4 \quad \Rightarrow \quad 4x = 16 \quad \Rightarrow \quad x = \frac{16}{4} = 46x−2x=12+4⇒4x=16⇒x=416=4
Q22. Solve the equation:
3x+5=4x+93x + 5 = 4x + 93x+5=4x+9
Solution:3x−4x=9−5⇒−x=4⇒x=−43x – 4x = 9 – 5 \quad \Rightarrow \quad -x = 4 \quad \Rightarrow \quad x = -43x−4x=9−5⇒−x=4⇒x=−4
Q23. Solve the equation:
5x+2=3x+125x + 2 = 3x + 125x+2=3x+12
Solution:5x−3x=12−2⇒2x=10⇒x=102=55x – 3x = 12 – 2 \quad \Rightarrow \quad 2x = 10 \quad \Rightarrow \quad x = \frac{10}{2} = 55x−3x=12−2⇒2x=10⇒x=210=5
Q24. Solve the equation:
4x+7=2x+154x + 7 = 2x + 154x+7=2x+15
Solution:4x−2x=15−7⇒2x=8⇒x=82=44x – 2x = 15 – 7 \quad \Rightarrow \quad 2x = 8 \quad \Rightarrow \quad x = \frac{8}{2} = 44x−2x=15−7⇒2x=8⇒x=28=4
Q25. Solve the equation:
8x+5=3x+258x + 5 = 3x + 258x+5=3x+25
Solution:8x−3x=25−5⇒5x=20⇒x=205=48x – 3x = 25 – 5 \quad \Rightarrow \quad 5x = 20 \quad \Rightarrow \quad x = \frac{20}{5} = 48x−3x=25−5⇒5x=20⇒x=520=4
Q26. Solve the equation:
6x−3=2x+96x – 3 = 2x + 96x−3=2x+9
Solution:6x−2x=9+3⇒4x=12⇒x=124=36x – 2x = 9 + 3 \quad \Rightarrow \quad 4x = 12 \quad \Rightarrow \quad x = \frac{12}{4} = 36x−2x=9+3⇒4x=12⇒x=412=3
Q27. Solve the equation:
5x−7=4x+115x – 7 = 4x + 115x−7=4x+11
Solution:5x−4x=11+7⇒x=185x – 4x = 11 + 7 \quad \Rightarrow \quad x = 185x−4x=11+7⇒x=18
Q28. Solve the equation:
3x+10=2x+133x + 10 = 2x + 133x+10=2x+13
Solution:3x−2x=13−10⇒x=33x – 2x = 13 – 10 \quad \Rightarrow \quad x = 33x−2x=13−10⇒x=3
Q29. Solve the equation:
7x+9=3x+257x + 9 = 3x + 257x+9=3x+25
Solution:7x−3x=25−9⇒4x=16⇒x=164=47x – 3x = 25 – 9 \quad \Rightarrow \quad 4x = 16 \quad \Rightarrow \quad x = \frac{16}{4} = 47x−3x=25−9⇒4x=16⇒x=416=4
Q30. Solve the equation:
8x−7=3x+138x – 7 = 3x + 138x−7=3x+13
Solution:8x−3x=13+7⇒5x=20⇒x=205=48x – 3x = 13 + 7 \quad \Rightarrow \quad 5x = 20 \quad \Rightarrow \quad x = \frac{20}{5} = 48x−3x=13+7⇒5x=20⇒x=520=4
Q31. Solve the equation:
5x−2=4x+35x – 2 = 4x + 35x−2=4x+3
Solution:5x−4x=3+2⇒x=55x – 4x = 3 + 2 \quad \Rightarrow \quad x = 55x−4x=3+2⇒x=5
Q32. Solve the equation:
9x+4=3x+229x + 4 = 3x + 229x+4=3x+22
Solution:9x−3x=22−4⇒6x=18⇒x=186=39x – 3x = 22 – 4 \quad \Rightarrow \quad 6x = 18 \quad \Rightarrow \quad x = \frac{18}{6} = 39x−3x=22−4⇒6x=18⇒x=618=3
Q33. Solve the equation:
2x+3=4x−52x + 3 = 4x – 52x+3=4x−5
Solution:2x−4x=−5−3⇒−2x=−8⇒x=−8−2=42x – 4x = -5 – 3 \quad \Rightarrow \quad -2x = -8 \quad \Rightarrow \quad x = \frac{-8}{-2} = 42x−4x=−5−3⇒−2x=−8⇒x=−2−8=4
Q34. Solve the equation:
6x−1=3x+86x – 1 = 3x + 86x−1=3x+8
Solution:6x−3x=8+1⇒3x=9⇒x=93=36x – 3x = 8 + 1 \quad \Rightarrow \quad 3x = 9 \quad \Rightarrow \quad x = \frac{9}{3} = 36x−3x=8+1⇒3x=9⇒x=39=3
Q35. Solve the equation:
4x+3=2x+194x + 3 = 2x + 194x+3=2x+19
Solution:4x−2x=19−3⇒2x=16⇒x=162=84x – 2x = 19 – 3 \quad \Rightarrow \quad 2x = 16 \quad \Rightarrow \quad x = \frac{16}{2} = 84x−2x=19−3⇒2x=16⇒x=216=8
Q36. Solve the equation:
6x−7=3x+116x – 7 = 3x + 116x−7=3x+11
Solution:6x−3x=11+7⇒3x=18⇒x=183=66x – 3x = 11 + 7 \quad \Rightarrow \quad 3x = 18 \quad \Rightarrow \quad x = \frac{18}{3} = 66x−3x=11+7⇒3x=18⇒x=318=6
Q37. Solve the equation:
7x+4=5x+147x + 4 = 5x + 147x+4=5x+14
Solution:7x−5x=14−4⇒2x=10⇒x=102=57x – 5x = 14 – 4 \quad \Rightarrow \quad 2x = 10 \quad \Rightarrow \quad x = \frac{10}{2} = 57x−5x=14−4⇒2x=10⇒x=210=5
Q38. Solve the equation:
8x−5=3x+158x – 5 = 3x + 158x−5=3x+15
Solution:8x−3x=15+5⇒5x=20⇒x=205=48x – 3x = 15 + 5 \quad \Rightarrow \quad 5x = 20 \quad \Rightarrow \quad x = \frac{20}{5} = 48x−3x=15+5⇒5x=20⇒x=520=4
Q39. Solve the equation:
4x+9=3x+144x + 9 = 3x + 144x+9=3x+14
Solution:4x−3x=14−9⇒x=54x – 3x = 14 – 9 \quad \Rightarrow \quad x = 54x−3x=14−9⇒x=5
Q40. Solve the equation:
3x−2=4x+13x – 2 = 4x + 13x−2=4x+1
Solution:3x−4x=1+2⇒−x=3⇒x=−33x – 4x = 1 + 2 \quad \Rightarrow \quad -x = 3 \quad \Rightarrow \quad x = -33x−4x=1+2⇒−x=3⇒x=−3
Q41. Solve the equation:
2x+4=3x+12x + 4 = 3x + 12x+4=3x+1
Solution:2x−3x=1−4⇒−x=−3⇒x=32x – 3x = 1 – 4 \quad \Rightarrow \quad -x = -3 \quad \Rightarrow \quad x = 32x−3x=1−4⇒−x=−3⇒x=3
Q42. Solve the equation:
9x−5=2x+259x – 5 = 2x + 259x−5=2x+25
Solution:9x−2x=25+5⇒7x=30⇒x=3079x – 2x = 25 + 5 \quad \Rightarrow \quad 7x = 30 \quad \Rightarrow \quad x = \frac{30}{7}9x−2x=25+5⇒7x=30⇒x=730
Q43. Solve the equation:
5x−4=3x+105x – 4 = 3x + 105x−4=3x+10
Solution:5x−3x=10+4⇒2x=14⇒x=142=75x – 3x = 10 + 4 \quad \Rightarrow \quad 2x = 14 \quad \Rightarrow \quad x = \frac{14}{2} = 75x−3x=10+4⇒2x=14⇒x=214=7
Q44. Solve the equation:
6x+3=4x+176x + 3 = 4x + 176x+3=4x+17
Solution:6x−4x=17−3⇒2x=14⇒x=142=76x – 4x = 17 – 3 \quad \Rightarrow \quad 2x = 14 \quad \Rightarrow \quad x = \frac{14}{2} = 76x−4x=17−3⇒2x=14⇒x=214=7
Q45. Solve the equation:
7x+5=3x+257x + 5 = 3x + 257x+5=3x+25
Solution:7x−3x=25−5⇒4x=20⇒x=204=57x – 3x = 25 – 5 \quad \Rightarrow \quad 4x = 20 \quad \Rightarrow \quad x = \frac{20}{4} = 57x−3x=25−5⇒4x=20⇒x=420=5
Q46. Solve the equation:
4x−3=2x+74x – 3 = 2x + 74x−3=2x+7
Solution:4x−2x=7+3⇒2x=10⇒x=102=54x – 2x = 7 + 3 \quad \Rightarrow \quad 2x = 10 \quad \Rightarrow \quad x = \frac{10}{2} = 54x−2x=7+3⇒2x=10⇒x=210=5
Q47. Solve the equation:
8x+9=3x+248x + 9 = 3x + 248x+9=3x+24
Solution:8x−3x=24−9⇒5x=15⇒x=155=38x – 3x = 24 – 9 \quad \Rightarrow \quad 5x = 15 \quad \Rightarrow \quad x = \frac{15}{5} = 38x−3x=24−9⇒5x=15⇒x=515=3
Q48. Solve the equation:
6x−2=4x+86x – 2 = 4x + 86x−2=4x+8
Solution:6x−4x=8+2⇒2x=10⇒x=102=56x – 4x = 8 + 2 \quad \Rightarrow \quad 2x = 10 \quad \Rightarrow \quad x = \frac{10}{2} = 56x−4x=8+2⇒2x=10⇒x=210=5
Q49. Solve the equation:
9x−4=2x+119x – 4 = 2x + 119x−4=2x+11
Solution:9x−2x=11+4⇒7x=15⇒x=1579x – 2x = 11 + 4 \quad \Rightarrow \quad 7x = 15 \quad \Rightarrow \quad x = \frac{15}{7}9x−2x=11+4⇒7x=15⇒x=715
Q50. Solve the equation:
5x+7=2x+185x + 7 = 2x + 185x+7=2x+18
Solution:5x−2x=18−7⇒3x=11⇒x=1135x – 2x = 18 – 7 \quad \Rightarrow \quad 3x = 11 \quad \Rightarrow \quad x = \frac{11}{3}5x−2x=18−7⇒3x=11⇒x=311
Q51. Solve the equation:
7x−8=3x+127x – 8 = 3x + 127x−8=3x+12
Solution:7x−3x=12+8⇒4x=20⇒x=204=57x – 3x = 12 + 8 \quad \Rightarrow \quad 4x = 20 \quad \Rightarrow \quad x = \frac{20}{4} = 57x−3x=12+8⇒4x=20⇒x=420=5
Q52. Solve the equation:
6x+2=4x+106x + 2 = 4x + 106x+2=4x+10
Solution:6x−4x=10−2⇒2x=8⇒x=82=46x – 4x = 10 – 2 \quad \Rightarrow \quad 2x = 8 \quad \Rightarrow \quad x = \frac{8}{2} = 46x−4x=10−2⇒2x=8⇒x=28=4
Q53. Solve the equation:
3x+4=5x+123x + 4 = 5x + 123x+4=5x+12
Solution:3x−5x=12−4⇒−2x=8⇒x=8−2=−43x – 5x = 12 – 4 \quad \Rightarrow \quad -2x = 8 \quad \Rightarrow \quad x = \frac{8}{-2} = -43x−5x=12−4⇒−2x=8⇒x=−28=−4
Q54. Solve the equation:
2x−3=4x+92x – 3 = 4x + 92x−3=4x+9
Solution:2x−4x=9+3⇒−2x=12⇒x=12−2=−62x – 4x = 9 + 3 \quad \Rightarrow \quad -2x = 12 \quad \Rightarrow \quad x = \frac{12}{-2} = -62x−4x=9+3⇒−2x=12⇒x=−212=−6
This is the end of Simple Linear Equations
Also Read: Class 8 Mathematics – Chapter 3: Linear Equations in Two Variables
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