Question

linear equations w/ distribution (lev 2)
question
solve for x.
2(2x + 5) + 4x - 4 = 30
answer
x =
submit answer

Explanation:

Step1: Distribute the 2

First, we distribute the 2 in \(2(2x + 5)\). Using the distributive property \(a(b + c)=ab + ac\), we get:
\(2\times2x + 2\times5 + 4x - 4 = 30\)
\(4x + 10 + 4x - 4 = 30\)

Step2: Combine like terms

Next, we combine the like terms (the \(x\)-terms and the constant terms).
For the \(x\)-terms: \(4x + 4x = 8x\)
For the constant terms: \(10 - 4 = 6\)
So the equation becomes:
\(8x + 6 = 30\)

Step3: Subtract 6 from both sides

We want to isolate the term with \(x\), so we subtract 6 from both sides of the equation:
\(8x + 6 - 6 = 30 - 6\)
\(8x = 24\)

Step4: Divide by 8

Finally, we divide both sides by 8 to solve for \(x\):
\(\frac{8x}{8}=\frac{24}{8}\)
\(x = 3\)

Answer:

\(3\)