Question

Given − 2(x − 10) = 14 , is x = 3 a solution? Explain why or why not.

Answer 1

If we have that the equation is:

`-2(x-10)=14`

We need to proceed as follows to find the value of x (there are many ways to solve it. One is as follows):

1. Apply the distributive property at the left side of the equation:

`-2(x)-2(-10)=14\Rightarrow-2x+20=14`

2. Subtract 20 from both sides of the equation:

`-2x+20-20=14-20\Rightarrow-2x=-6`

3. Divide both sides by -2:

`-(2x)/(-2)=-(6)/(-2)\Rightarrow x=3`

If we substitute this value into the original equation, we have:

`-2(3-10)=14\Rightarrow-2(-7)=14\Rightarrow14=14`

Therefore, we have that x = 3 is a solution of the equation:

`-2(x-10)=14`

After solving the equation, and then by checking the correctness of the value, we have that x = 3.

In summary, x = 3 is a solution.