Yuto solved the equation below.

Question

Negative 2 (x + 5) = negative 2 (x minus 2) + 5

What is the solution to Yuto’s equation?
–10
9
no solution
infinitely many solutions

Answer 1

To solve the equation \(-2(x + 5) = -2(x - 2) + 5\), we first distribute the \(-2\) on both sides:

\[ -2(x + 5) = -2x - 10 \] \[ -2(x - 2) + 5 = -2x + 4 + 5 = -2x + 9 \]

Now the equation can be rewritten as:

\[ -2x - 10 = -2x + 9 \]

Next, we will add \(2x\) to both sides:

\[ -10 = 9 \]

This statement \(-10 = 9\) is not true. Since we arrived at a contradiction, this implies that there is no solution for the equation.

Thus, the answer is:

no solution.