Question

question
solve for x:
$x + 4 = -9 - 3(x - 5) + 8x$

Explanation:

Step1: Expand the right - hand side

First, we use the distributive property \(a(b + c)=ab+ac\) to expand \(-3(x - 5)\). We get \(-3x+15\). So the equation becomes \(x + 4=-9-3x + 15+8x\).

Step2: Combine like terms on the right - hand side

Combine the \(x\) - terms and the constant terms on the right - hand side. The \(x\) - terms: \(-3x+8x = 5x\). The constant terms: \(-9 + 15=6\). So the equation is now \(x + 4=5x+6\).

Step3: Move the \(x\) - terms to one side

Subtract \(x\) from both sides of the equation: \(x+4 - x=5x + 6-x\). This simplifies to \(4 = 4x+6\).

Step4: Move the constant terms to the other side

Subtract 6 from both sides: \(4-6=4x+6 - 6\). We get \(-2 = 4x\).

Step5: Solve for \(x\)

Divide both sides by 4: \(x=\frac{-2}{4}=-\frac{1}{2}\).

Answer:

\(x =-\frac{1}{2}\)