# Exercise 2.1

Exercise 2.10 %

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

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

Substuite x in equation.

: 3 × 18 = 2 × 8 ⟹ = + 18 ⟹ = .

So, LHS to RHS.

**2. 5 t −3 = 3t−5**

⟹ 2t = − 2 ⟹ t=− 2 2 ⟹ t = .

Substitute T in equation.

⟹5 t − 3 = 3 t − 5 ⟹ 5( )-3 = 3( )-5

⟹ -5-3 ⟹ -3-5 ⟹ = .

So, LHS to RHS.

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

Substract 3x in both sides: 5 x − 3 x + 9 = 5 + 3 x − 3 x ⟹ 2 x + 9 = 5

Subtract 9 from both sides: 2 x + 9 − 9 = 5 − 9 ⟹ 2x = .

Divide both sides by 2 to solve: 2 x 2 = − 4 2 ⟹ x = .

Substitute x in the equation.

5 ( ) + 9 = 5 + 3( ) ⟹ − 10 + 9 = 5 − 6 ⟹ = .

So, LHS to RHS.

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

Subtract 2z from both sides: 4 z − 2 z + 3 = 6 + 2 z − 2 z ⟹ 2 z + 3 = 6

Substract 3 from both sides: 2 z + 3 − 3 = 6 − 3 ⟹ 2 z = 3

Divide both sides by 2 2 z 2 = 3 2 ⟹ z = 3 2 .

Substitute z in Equation

4( ) + 3 = 6 + 2( ) ⇒ 6 + 3 = 6 + 3 ⇒ = .

So, LHS to RHS.

**5. 2 x −1= 14−x**

Add x to both sides: 2 x + x − 1 = 14 − x + x ⇒ 3x - = 14.

Add 1 to both sides: 3 x − 1 + 1 = 14 + 1 ⇒ 3x =

Divide both sides by 3: 3 x 3 = 15 3 ⇒ x =

Substitute x in Equation

2 × - 1 = 14 − 5 ⇒ 10 − 1 = 9 ⇒ =

So, LHS to RHS.

**6. 8 x +4 = 3 x−1+7**

Distribute the 3 on the right side: 8 x + 4 = 3 x − 3 + 7 .

Combine like terms on the right side: 8 x + 4 = 3 x + 4 .

Subtract 3x from both sides: 8 x − 3 x + 4 = 4 ⇒ 5 x + 4 = 4

Subtract 4 from both sides: 5 x + 4 − 4 = 4 − 4 ⇒ 5x = 0.

Divide both sides by 5: 5 x 5 = 0 5 ⇒ x = .

⟹ 8 × + 4 = 3 ( -1) + 7 ⇒ 4 = 3 − 1 + 7 ⇒ 4 = 3 − 1 + 7 ⇒ 4 = − 3 + 7 ⇒ = .

So, LHS to RHS.

**7. x = **

Expanding RHS: x = 4 x 5 + 8

Subtract 4 x 5 from both sides: x − 4 x 5 = 8 ⇒ x 5 = 8.

Multiply both sides by 5: x = 5 × 8 ⇒ x = .

Substitute x in Equation.

40 = 4 5 × 40 + 10 ⇒ 40 = 4 5 × 50 ⇒ = .

So, LHS to RHS.

**8. 2**

Subtract 1 from both sides: 2 x 3 + 1 - 1 = 7 x 15 + 3 - 1 ⇒ 2 x 3 = 7 x 15 + 2.

Subtract 7 x 15 from both sides: 2 x 3 - 7 x 15 = 2

Find common denominator: 10 x 15 - 7 x 15 = 2 ⇒ 3 x 15 = 2.

Simplify the Equation: 3 x 15 = 2 ⇒ x 5 = 2.

Multiply both sides by 5: x = 2 × 5 ⇒ x = .

Substitute x in Equation.

2 × /3 + 1 = 7 × /15 + 3 ⇒ 20 3 + 1 = 70 15 + 3

Convert 70 15 to a common denominator: 20 3 + 1 = 14 3 + 3 ⇒ 20 3 + 3 3 = 14 3 + 9 3 ⇒ / = /

So, LHS to RHS.

**9. 2 y +**

Simplify the equation 2 y + y + 5 3 = 26 3 ⇒ 3 y + 5 3 = 26 3 ⇒ 3y = /

3y = 21 3 ⇒ 3y = 7 ⇒ y = / .

Substitute y in Equation.

So, LHS to RHS.

**10. 3 m = 5m**

Substract 5m from both sides 3 m − 5 m = 5 m − 5 m − 8 5 ⇒ − 2 m = − 8 5 .

Divide both sides by -2 to slove for m − 2 m − 2 = − 8 5 − 2 ⇒ m = / .

Substitute m in Equation.

So, LHS to RHS.