Question

question 4 of 10
what is the solution to this equation?
4x + 2(x + 6) = 36
a. x = 7
b. x = 8
c. x = 5
d. x = 4

Explanation:

Step1: Expand the bracket

First, we expand the \(2(x + 6)\) term. Using the distributive property \(a(b + c)=ab+ac\), we get \(2(x + 6)=2x+12\). So the equation becomes \(4x + 2x+12 = 36\).

Step2: Combine like terms

Next, we combine the \(x\) terms. \(4x+2x = 6x\), so the equation is now \(6x+12 = 36\).

Step3: Subtract 12 from both sides

We subtract 12 from both sides to isolate the term with \(x\). So \(6x+12 - 12=36 - 12\), which simplifies to \(6x = 24\).

Step4: Divide both sides by 6

Finally, we divide both sides by 6 to solve for \(x\). \(\frac{6x}{6}=\frac{24}{6}\), which gives \(x = 4\). Wait, no, wait, let's check again. Wait, \(36-12 = 24\)? Wait, no, \(36 - 12=24\)? Wait, no, \(36-12 = 24\)? Wait, no, \(36-12 = 24\)? Wait, no, I made a mistake. Wait, \(36-12 = 24\)? Wait, no, \(36-12 = 24\)? Wait, no, let's recalculate. Wait, the original equation: \(4x+2(x + 6)=36\). Expand: \(4x+2x + 12=36\). Combine like terms: \(6x+12 = 36\). Subtract 12: \(6x=36 - 12=24\). Then \(x = 24\div6 = 4\)? Wait, but let's check with the options. Option D is \(x = 4\). Wait, but let's verify by plugging \(x = 4\) back into the original equation. Left side: \(4(4)+2(4 + 6)=16+2(10)=16 + 20=36\), which equals the right side. So that's correct. Wait, but earlier when I thought I made a mistake, but no, it's correct. Wait, but let's check the other options. For \(x = 7\): \(4(7)+2(7 + 6)=28+2(13)=28 + 26=54
eq36\). For \(x = 8\): \(4(8)+2(8 + 6)=32+2(14)=32 + 28=60
eq36\). For \(x = 5\): \(4(5)+2(5 + 6)=20+2(11)=20 + 22=42
eq36\). For \(x = 4\): \(4(4)+2(4 + 6)=16+2(10)=16 + 20=36\), which matches. So the correct answer is D.

Answer:

D. \(x = 4\)