Question

solve and check the linear equation. 4(x - 5) - 5(x - 4) = x + 4 - (x - 6)
what is the solution?
○ a. the solution set is {}

Explanation:

Step1: Expand both sides

Expand $4(x - 5)-5(x - 4)$ and $x + 4-(x - 6)$.
$4(x - 5)-5(x - 4)=4x-20-5x + 20=-x$.
$x + 4-(x - 6)=x + 4-x + 6=10$.

Step2: Solve for x

Set the two - expanded expressions equal:
$-x=10$, so $x=-10$.

Step3: Check the solution

Substitute $x = - 10$ into the original equation.
Left - hand side: $4(-10 - 5)-5(-10 - 4)=4\times(-15)-5\times(-14)=-60 + 70 = 10$.
Right - hand side: $-10+4-(-10 - 6)=-10 + 4+10 + 6=10$.
Since the left - hand side equals the right - hand side when $x=-10$, the solution is correct.

Answer:

A. The solution set is $\{-10\}$