Question

Solve each of the following equations by first using the distributive property to rewrite one or both of the two sides of the equation.

(A) 2(5t+9)=36-7(t-2)+t
(B) 47+s=8(s+2)-s+13

Answer 1

A) t = 2

B) s = 3

Explanation:

(A) 2(5t+9)=36-7(t-2)+t

• Expand 2(5t + 9) using distributive law
  
  `2(5t + 9) = 2 \cdot 5t + 2 \cdot 9 = 10t + 18`
  
• Expand -7(t-2) using distributive law
  
  `7(t-2) = -7 \cdot t - (-7) \cdot 2 = -7t + 14`
  
• simplify
  `36-7\left(t-2\right)+t`
  
  `36-7\left(t-2\right)+t = 36-7t+14+t = -6t+50`
  
• Set lhs = rhs
  
  `10t+18=-6t+50`
  
• Subtract 18 from both sides
  
  `0t+18-18=-6t+50-18`
  
• Simplify
  
  `10t=-6t+32`
  
• Add 6t to both sides
  
  `0t+6t=-6t+32+6t`
  
• Simplify
  
  `16t=32`
• Divide by 16 both sides
  
  
  `(16t)/(16)=(32)/(16)`
  

• ==> t = 2 (answer A)
  
  
  

(B) 47+s=8(s+2)-s+13

• 8(s+2) = 8s + 16

• RHS becomes 8s + 16 - s + 13
  ==> 7s + 29

• We get
  47 + s = 7s + 29

• Subtract s from both sides
  ⇒ 47 = 7s - s + 29
  ⇒ 47 = 6s + 29

• Subtract 29 from both sides
  47 - 29 = 6s
  18 = 6s

• Divide both sides by 6
  ⇒ 18/6 = 6s/6
  ⇒ 3 = s
  or s = 3