Problem 45

Question

Solve each equation using both the addition and multiplication properties of equality. Check proposed solutions. $$-5 x=-2 x-12$$

Step-by-Step Solution

Verified
Answer
The solution to the equation \(-5x = -2x - 12\) is \(x = 4\)
1Step 1: Isolate x terms on one side of the equation
First, add \(2x\) to both sides of the equation to get rid of the \(x\) on the right hand side. This gives us \(-5x + 2x = -12\), which simplifies to \(-3x = -12\).
2Step 2: Solve for x
Next, we divide every term by \(-3\) to solve for \(x\). This gives \(x = 4\).
3Step 3: Check the solution
We substitute 4 into the original equation \(-5x = -2x - 12\). This gives \(-5(4) = -2(4) - 12\) which simplifies to \(-20 = -8 - 12\), and further simplifies to \(-20 = -20\). Since both sides are equal, our solution is correct.