Question

1. solve this equation for x: \\( 4(4x + 6) + 3x = 81 \\) enter each line of work as an equation. enter your next step here

Explanation:

Step1: Distribute the 4

First, we use the distributive property to expand \(4(4x + 6)\). The distributive property states that \(a(b + c)=ab+ac\), so applying that here we get \(4\times4x+4\times6\), which simplifies to \(16x + 24\). Now our equation becomes:
\(16x + 24+3x = 81\)

Step2: Combine like terms

Next, we combine the \(x\)-terms. We have \(16x\) and \(3x\), so adding those together gives \((16x + 3x)+24 = 81\), which simplifies to \(19x+24 = 81\)

Step3: Subtract 24 from both sides

To isolate the term with \(x\), we subtract 24 from both sides of the equation. So we do \(19x + 24-24=81 - 24\), which simplifies to \(19x=57\)

Step4: Divide by 19

Finally, we divide both sides of the equation by 19 to solve for \(x\). So \(\frac{19x}{19}=\frac{57}{19}\), which gives \(x = 3\)

Answer:

\(x = 3\)