Question

linear equations w/ distribution (lev 2)
score: 7/10 penalty: 0.5 off
question
solve for x.
$-2(5x + 2) + 5x + 2 = 23$

Explanation:

Step1: Apply the distributive property

First, we distribute the -2 across the terms inside the parentheses. The distributive property states that \(a(b + c)=ab+ac\). So, for \(-2(5x + 2)\), we get \(-2\times5x+(-2)\times2=-10x - 4\).
The equation becomes: \(-10x-4 + 5x+2=23\)

Step2: Combine like terms

Next, we combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(-10x+5x=-5x\). For the constant terms: \(-4 + 2=-2\).
The equation simplifies to: \(-5x-2=23\)

Step3: Isolate the variable term

We add 2 to both sides of the equation to isolate the term with \(x\). Using the addition property of equality (if \(a = b\), then \(a + c=b + c\)), we have:
\(-5x-2 + 2=23 + 2\)
Simplifying both sides gives: \(-5x=25\)

Step4: Solve for \(x\)

We divide both sides of the equation by -5 to solve for \(x\). Using the division property of equality (if \(a = b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\)), we get:
\(\frac{-5x}{-5}=\frac{25}{-5}\)
Simplifying both sides gives: \(x=-5\)

Answer:

\(x = - 5\)