Question

Given the equation : 5 + x - 12 = x - 7Part A. Solve the equation 5 + x - 12 = x - 7 In your final answer, be sure to state the solution and include all of your work.Part B. Use the values x = -4, 0, 5 to verify your solution to the equation 5 + x - 12 = x - 7 In your final answer, include all of your calculations.

Answer 1

Part A: Given the equation : 5 + x - 12 = x - 7

Solve the equation,

$\begin{gathered} 5+x-12=x-7 \\ \text{take left hand side of equation,} \\ \text{LHS}=5+x-12 \\ =x-7 \\ =\text{RHS} \end{gathered}$

Hence, it proves that 5 + x - 12 = x - 7

Part B: for x=-4

$\begin{gathered} \text{LHS}=5+x-12 \\ =5-4-12 \\ =-11 \\ \text{Take RHS,} \\ \text{RHS}=x-7 \\ =-4-7-11 \\ \text{hence, LHS=RHS for x=-4} \end{gathered}$

For x=0,

$\begin{gathered} \text{LHS}=5+x-12 \\ =5+0-12 \\ =-7 \\ \text{RHS}=x-7 \\ =0-7 \\ =-7 \\ \text{hence, LHS=RHS for x=0} \end{gathered}$

For x=5,

$\begin{gathered} \text{LHS}=5+x-12 \\ =5+5-12 \\ =-2 \\ \text{RHS}=x-7 \\ =5-7 \\ =-2 \\ \text{Hence, LHS=RHS for x=5} \end{gathered}$

Answer: The euation is : 5 + x - 12 = x - 7

The values of x =-4,0,5 all satisfies the given equation.