Question

4.
13 - 4(3x - 4) = 29 + 4(5x + 2)

x = -\frac{1}{4} \t x = -4 \t x = 4
maroon \t lime green \t white

Explanation:

Step1: Expand the brackets

First, we expand the terms with brackets on both sides of the equation. Using the distributive property \(a(b + c)=ab+ac\), we have:
Left side: \(13-4(3x - 4)=13-(12x - 16)=13 - 12x+16\)
Right side: \(29 + 4(5x + 2)=29+20x + 8\)
So the equation becomes \(13 - 12x+16=29+20x + 8\)

Step2: Combine like terms

Combine the constant terms on both sides.
Left side: \(13 + 16-12x=29-12x\)
Right side: \(29 + 8+20x=37+20x\)
Now the equation is \(29-12x=37+20x\)

Step3: Move the variable terms to one side

Add \(12x\) to both sides to get all the \(x\) terms on one side:
\(29-12x + 12x=37+20x+12x\)
Simplifies to \(29=37 + 32x\)

Step4: Solve for \(x\)

Subtract 37 from both sides:
\(29-37=37 + 32x-37\)
\(-8 = 32x\)
Then divide both sides by 32:
\(x=\frac{-8}{32}=-\frac{1}{4}\)

Answer:

\(x = -\frac{1}{4}\) (maroon)