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**EXERCISE 2.3 **

**Ques: ****Solve the following equations and check your results.**

1. 3x = 2x + 18

2. 5t â€“ 3 = 3t â€“ 5

3. 5x + 9 = 5 + 3x

4. 4z + 3 = 6 + 2z

5. 2x â€“ 1 = 14 â€“ x

6. 8x + 4 = 3(x â€“ 1) + 7

7.

8.

9.

10. 3m = 5m - 8/5

**Ans: ****1.** 3x = 2x + 18

Transposing 2x from RHS to LHS, we have

3x â€“ 2x = 18

â‡’ x = 18

**2.** 5t â€“ 3 = 3t â€“ 5

Transposing (â€“3) to RHS, we have

5t = 3t â€“ 5 + 3

â‡’ 5t = 3t â€“ 2

Transposing 3t to LHS, we have

5t â€“ 3t = â€“2

â‡’ 2t = â€“2

Diving both sides by 2, we have

t = â€“1

**3.** 5x + 9 = 5 + 3x

Transposing 9 to RHS, we have

5x = 5 + 3x â€“ 9

â‡’ 5x = â€“4 + 3x

Transposing 3x to LHS, we have

5x â€“ 3x = â€“4

â‡’ 2x = â€“4

Dividing both sides by 2, we have

x = -4/2 = -2

x = -2

**4. **4z + 3 = 6 + 2z

Transposing 3 to RHS, we have

4z = 6 â€“ 3 + 2z

â‡’ 4z = 3 + 2z

Transposing 2z to LHS, we have

4z â€“ 2z = 3

â‡’ 2z = 3

Dividing both sides by 2, we have

z = 3/2

**5.** 2x â€“ 1 = 14 â€“ x

Transposing (â€“1) to RHS, we have

2x = 14 â€“ x + 1

â‡’ 2x = 15 â€“ x

Transposing (â€“x) to LHS, we have

2x + x = 15**â‡’ **3x = 15

Dividing both sides by 3, we have

x = 15/3 = 5

âˆ´ x = 5

**6.** 8x + 4 = 3(x â€“ 1) + 7

8x + 4 = 3x â€“ 3 + 7

â‡’ 8x + 4 = 3x + 4

Transposing 4 to RHS, we have

8x = 3x + 4 â€“ 4

Transposing 3x to LHS, we have

8x â€“ 3x = 0

â‡’ 5x = 0

âˆ´ x = 0

**7. **

Using distributive property,

â‡’

Transposing x to LHS, we have

â‡’

â‡’ x/5 = 8

Multiplying both sides by 5, we have

x = 8 Ã— 5 = 40

âˆ´ x = 40

**8. **

Transposing 1 to RHS, we have

â‡’

Transposing 7x/15 to LHS, we have

â‡’

â‡’ 3x/15 = 2

Multiplying both sides by 15, we have

3x = 2 Ã— 15 = 30

Dividing both sides by 3, we have

âˆ´ x = 10

**9. **

Transposing 5/3 to RHS, we have

Transposing (â€“y) to LHS, we have

â‡’ 3y = 7

Dividing both sides by 3, we have

3y = 3 = 7/3

âˆ´ y = 7/3

**10.** 3m = 5m

Transposing 5m to LHS, we have

3m - 5m =

â‡’ -2m =

Dividing both sides by (â€“2), we have

âˆ´ m = 4/5

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