Question

When Justin solved the following equation onThis Algebra Exam, he got a solution of x = -15.Was Justin correct? Justify your reasoning.3x + 5 = -2x - 10

Answer 1

x = -3

Given:

3x + 5 = -2x - 10

Let's solve for x.

3x + 5 = -2x - 10



Subtract both sides by 5:

3x + 5 - 5 = -2x - 10 - 5

3x = -2x - 15

Add 2x to both sides;

3x + 2x = -2x + 2x - 15

5x = -15

Divide both sides by 5:

`\begin{gathered} (5x)/(5)\text{ = - }(15)/(5) \\ \\ x\text{ = -3} \end{gathered}`

Since we got x =-3, Justin was wrong.

To justify this, substitute -15 for x in the equation:

3x + 5 = -2x - 10



3(-15) + 5 = -2(-15) - 10

-45 + 5 = 30 - 10

-40 = 20

Since the left hand side doesn't equate to the right hand side, x is not equal to -15.

Substitute -3 for x in the equation:

3x + 5 = -2x - 10



3(-3) + 5 = -2(-3) - 10

-9 + 5 = 6 - 10

-4 = -4

Since the right hand side and the left hand side of the equation are equal, x = -3