Question

1. for what value of x is the equation below true?

2 - 7(x + 3) - 10x = 15
a. -2
b. 2
c. 8/3
d. -8/17

Explanation:

Step1: Expand the bracket

First, we expand \(-7(x + 3)\) using the distributive property \(a(b + c)=ab+ac\). So \(-7(x + 3)=-7x-21\). The equation becomes:
\(2-7x - 21-10x=15\)

Step2: Combine like terms

Combine the \(x\)-terms and the constant terms. The \(x\)-terms are \(-7x\) and \(-10x\), so \(-7x-10x=-17x\). The constant terms are \(2\) and \(-21\), so \(2 - 21=-19\). The equation now is:
\(-17x-19 = 15\)

Step3: Isolate the \(x\)-term

Add \(19\) to both sides of the equation to isolate the term with \(x\).
\(-17x-19 + 19=15 + 19\)
Simplifying both sides, we get:
\(-17x=34\)

Step4: Solve for \(x\)

Divide both sides of the equation by \(-17\) to solve for \(x\).
\(x=\frac{34}{-17}\)
Simplifying the fraction, we find \(x = - 2\)

Answer:

a. -2