Exercise 2.1
Solve the following equations and check your results.
1. 3 x = 2 x + 18
Substituting x in equation: 3 x = 2 x + 18 ⟹ 3( ) = 2( ) + 18.
So, LHS to RHS.
2. 5 t − 3 = 3 t − 5
⟹ 2t = − 2 ⟹ t =− 2 2 ⟹ t =
Substituting 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 + 3 x
Substracting 3x in both sides: 5 x − 3 x + 9 = 5 + 3 x − 3 x ⟹ 2 x + 9 = 5
Subtracting 9 from both sides: 2 x + 9 − 9 = 5 − 9 ⟹ 2x =
Dividing both sides by 2 to solve: 2 x 2 = − 4 2 ⟹ x =
Substituting x in the equation: 5 ( ) + 9 = 5 + 3( )
So, LHS to RHS.
4. 4 z + 3 = 6 + 2 z
Subtracting 2z from both sides: 4 z − 2 z + 3 = 6 + 2 z − 2 z ⟹ 2 z + 3 = 6
Substracting 3 from both sides: 2 z + 3 − 3 = 6 − 3 ⟹ 2 z =
Dividing both sides by 2: 2 z 2 = 3 2 ⟹ z =
Substituting in equation: 4( ) + 3 = 6 + 2( )
6 + 3 = 6 + 3 ⇒ =
So, LHS to RHS.
5. 2 x − 1 = 14 − x
Adding x to both sides: 2 x + x − 1 = 14 − x + x ⇒ 3x - =
Adding 1 to both sides: 3 x − 1 + 1 = 14 + 1 ⇒ 3x =
Dividing both sides by 3: 3 x 3 = 15 3 ⇒ x =
Substituting x in equation: 2 × - 1 = 14 − 5
⇒ 10 − 1 = 9 ⇒ =
So, LHS to RHS.
6. 8 x + 4 = 3 x − 1 + 7
Distributing the 3 on the right side: 8 x + 4 = 3 x − 3 + 7
Combining like terms on the right side: 8 x + 4 = 3 x + 4
Subtracting 3x from both sides: 8 x − 3 x + 4 = 4 ⇒ 5 x + 4 =
Subtracting 4 from both sides: 5 x + 4 − 4 = 4 − 4 ⇒ 5x =
Dividing both sides by 5: 5 x 5 = 0 5 ⇒ x =
Substituting in equation: 8 × + 4 = 3 ( -1) + 7 ⇒ 4 = 3 − 1 + 7 ⇒ 4 = 3 − 1 + 7 ⇒ 4 = − 3 + 7 ⇒ = .
So, LHS to RHS.
7. x = 4 x + 10 5
Expanding RHS: x = 4 x 5 + 8
Subtracting 4 x 5 from both sides: x − 4 x 5 = 8 ⇒ = 8
Multiplying both sides by 5: x = 5 × 8 ⇒ x =
Substituting x in equation: 40 = 4 5 × 40 + 10
40 = 4 5 × 50 ⇒ =
So, LHS to RHS.
8. 2 x 3 + 1 = 7 x 15 + 3
Subtracting 1 from both sides: 2 x 3 + 1 - 1 = 7 x 15 + 3 - 1 ⇒ 2 x 3 = 7 x 15 + 2.
Subtracting 7 x 15 from both sides: 2 x 3 - 7 x 15 = 2
Finding common denominator: 10 x 15 - 7 x 15 = 2 ⇒ = 2.
Simplify the Equation: 3 x 15 = 2 ⇒ = 2.
Multiplying both sides by 5: x = 2 × 5 ⇒ x = .
Substituting 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 + 5 3 = 26 3 − y
Simplifying the equation: 2 y + y + 5 3 = 26 3 ⇒ 3 y + 5 3 = 26 3 ⇒ 3y = /
3y = 21 3 ⇒ 3y = 7 ⇒ y =
Substituting y in equation: 2 7 3 + 5 3 = 26 3 -
⇒ 14 3 + 5 3 = 19 3 ⇒ =
So, LHS to RHS.
10. 3 m = 5 m − 8 5
Subtracting 5m from both sides: 3 m − 5 m = 5 m − 5 m − 8 5 ⇒ − 2 m = − 8 5
Dividing both sides by − 2 : − 2 m − 2 = − 8 5 − 2 ⇒ m =
Substituting m in equation: 3 × 4 5 = 5 × 4 5 - 8 5
⇒ 12 5 = 20 5 - 8 5 ⇒ =
So, LHS to RHS.