Question

linear equations w/ distribution (lev 2)
score: 0/3 penalty: none
question
solve for x.
4(5x + 3) - 2x + 2 = 32
answer attempt 1 out of 4
x =
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Explanation:

Step1: Distribute the 4

We start by applying the distributive property to \(4(5x + 3)\). The distributive property states that \(a(b + c)=ab+ac\), so we have:
\(4\times5x+4\times3 - 2x + 2 = 32\)
\(20x+12 - 2x + 2 = 32\)

Step2: Combine like terms

Next, we combine the \(x\)-terms and the constant terms. For the \(x\)-terms: \(20x-2x = 18x\). For the constant terms: \(12 + 2 = 14\). So the equation becomes:
\(18x+14 = 32\)

Step3: Subtract 14 from both sides

To isolate the term with \(x\), we subtract 14 from both sides of the equation. This gives:
\(18x+14 - 14 = 32 - 14\)
\(18x = 18\)

Step4: Divide by 18

Finally, we divide both sides of the equation by 18 to solve for \(x\):
\(\frac{18x}{18}=\frac{18}{18}\)
\(x = 1\)

Answer:

\(x = 1\)