Question

equation for x:
$-5(x - 6) - 2 = 5 + (x - 1)$
as a fraction if necessary.
swer below:

Explanation:

Step1: Expand the brackets

First, we expand the left - hand side and the right - hand side of the equation. For the left - hand side, using the distributive property \(a(b - c)=ab - ac\), we have \(-5(x - 6)=-5x+30\). So the left - hand side of the equation \(-5(x - 6)-2\) becomes \(-5x + 30-2=-5x+28\). For the right - hand side, we expand \(5+(x - 1)=5+x - 1=x + 4\). Now our equation is \(-5x+28=x + 4\).

Step2: Move the terms with x to one side

We can add \(5x\) to both sides of the equation to get rid of the \(-5x\) on the left - hand side. \(-5x+28 + 5x=x + 4+5x\), which simplifies to \(28 = 6x+4\).

Step3: Solve for x

Next, we subtract 4 from both sides of the equation. \(28-4=6x+4 - 4\), so \(24 = 6x\). Then we divide both sides by 6: \(\frac{24}{6}=\frac{6x}{6}\), which gives \(x = 4\).

Answer:

\(x = 4\)