NCERT CLASS 8TH MATHS CHAPTER 2 LINEAR EQUATIONS IN ONE VARIABLE

 CHAPTER 2

Linear Equations in One Variables

ONLINE CLASS 

Exercise 2.1

Solve the following equations and check your results.

1. 3x = 2x + 18

Subtract 2x from both sides:

3x − 2x = 18

✅ x = 18

2. 5t − 3 = 3t − 5

Subtract 3t from both sides:

2t − 3 = −5

Add 3 to both sides:

2t = −2

✅ t = −1

3. 5x + 9 = 5 + 3x

Subtract 3x from both sides:

2x + 9 = 5

Subtract 9:

2x = −4

✅ x = −2

4. 4z + 3 = 6 + 2z

Subtract 2z:

2z + 3 = 6

Subtract 3:

2z = 3

✅ z = 3/2

5. 2x − 1 = 14 − x

Add x to both sides:

3x − 1 = 14

Add 1:

3x = 15

✅ x = 5

6. 8x + 4 = 3(x − 1) + 7

Expand right side:

8x + 4 = 3x − 3 + 7

Simplify:

8x + 4 = 3x + 4

Subtract 3x and 4:

5x = 0

✅ x = 0

7. x = (4/5)(x + 10)

Expand:

x = (4/5)x + 8

Subtract (4/5)x:

(1/5)x = 8

Multiply by 5:

✅ x = 40

8. (2x/3) + 1 = (7x/15) + 3

Multiply all by 15 to clear denominators:

10x + 15 = 7x + 45

Simplify:

3x = 30

✅ x = 10

9. 2y + (5/3) = (26/3) − y

Multiply by 3:

6y + 5 = 26 − 3y

Simplify:

9y = 21

✅ y = 7/3

10. 3m = 5m − (8/5)

Subtract 5m:

−2m = −(8/5)

Divide by −2:

✅ m = 4/5

EXERCISE 2.2

Solve the following linear equations. 

1

$$\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}$$

Take the LCM of denominators → 2, 3, 4, 5 → LCM = 60

Multiply through by 60:

$$30x - 12 = 20x + 15$$

Simplify:

$$30x - 20x = 15 + 12$$ $$10x = 27$$

✅ x = 27/10 = 2.7

2.

$$\frac{n}{2} - \frac{3n}{4} + \frac{5n}{6} = 21$$

LCM of (2, 4, 6) = 12

Multiply by 12:

$$6n - 9n + 10n = 252$$ $$7n = 252$$

✅ n = 36

3.

$$x + 7 - \frac{8x}{3} = \frac{17}{6} - \frac{5x}{2}$$

LCM of denominators (3, 6, 2) = 6

Multiply through by 6:

$$6x + 42 - 16x = 17 - 15x$$

Simplify:

$$6x - 16x + 15x = 17 - 42$$ $$5x = -25$$

✅ x = -5

4

$$\frac{x - 5}{3} = \frac{x - 3}{5}$$

Cross multiply:

$$5(x - 5) = 3(x - 3)$$ $$5x - 25 = 3x - 9$$ $$2x = 16$$

✅ x = 8

5

$$\frac{3t - 2}{4} - \frac{2t + 3}{3} = \frac{2}{3} - t$$

LCM of (3, 4) = 12

Multiply by 12:

$$3(3t - 2) - 4(2t + 3) = 4(2) - 12t$$

Simplify:

$$9t - 6 - 8t - 12 = 8 - 12t$$ $$t - 18 = 8 - 12t$$ $$t + 12t = 8 + 18$$ $$13t = 26$$

✅ t = 2

6

$$m - \frac{m - 1}{2} = 1 - \frac{m - 2}{3}$$

LCM of (2, 3) = 6

Multiply by 6:

$$6m - 3(m - 1) = 6 - 2(m - 2)$$

Simplify:

$$6m - 3m + 3 = 6 - 2m + 4$$ $$3m + 3 = 10 - 2m$$ $$5m = 7$$

✅ m = 7/5 = 1.4

Simplify and solve the following linear equations.

7

$$3(t-3)=5(2t+1)$$

Expand:

$$3t-9=10t+5$$$$-9-5=10t-3t$$$$-14=7t$$

✅ t = -2

8

$$15(y-4)-2(y-9)+5(y+6)=0$$

Expand:

$$15y-60-2y+18+5y+30=0$$

Simplify:

$$(15y-2y+5y)+(-60+18+30)=0$$$$18y-12=0$$

✅ y = 12/18 = 2/3

9

$$3(5z-7)-2(9z-11)=4(8z-13)-17$$

Expand:

$$15z-21-18z+22=32z-52-17$$

Simplify:

$$-3z+1=32z-69$$$$-3z-32z=-69-1$$$$-35z=-70$$

✅ z = 2

10

$$0.25(4f-3)=0.05(10f-9)$$

Expand:

$$1f-0.75=0.5f-0.45$$

Simplify:

$$f-0.5f=-0.45+0.75$$$$0.5f=0.3$$

✅ f = 0.6