Question

question
solve for x.
-3(-2x - 4) - x + 4 = 41
answer attempt 1 out of 2
x =

Explanation:

Step1: Expand the left - hand side

First, we expand \(-3(-2x - 4)\) using the distributive property \(a(b + c)=ab+ac\). Here \(a=-3\), \(b = - 2x\) and \(c=-4\), so \(-3(-2x-4)=(-3)\times(-2x)+(-3)\times(-4)=6x + 12\).
The original equation \(-3(-2x - 4)-x + 4 = 41\) becomes \(6x+12 - x+4=41\).

Step2: Combine like terms

Combine the \(x\) terms and the constant terms. For the \(x\) terms: \(6x-x = 5x\). For the constant terms: \(12 + 4=16\). So the equation simplifies to \(5x+16 = 41\).

Step3: Isolate the variable term

Subtract 16 from both sides of the equation. According to the subtraction property of equality, if \(a=b\), then \(a - c=b - c\). So we have \(5x+16-16=41 - 16\), which simplifies to \(5x=25\).

Step4: Solve for \(x\)

Divide both sides of the equation \(5x = 25\) by 5. According to the division property of equality, if \(a=b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\). So \(\frac{5x}{5}=\frac{25}{5}\), which gives \(x = 5\).

Answer:

\(x = 5\)