Question

equations - solve for the given variable: 5 - (x - 4) = 3 (x + 2) type in the numerical answer only

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the equation \(5-(x - 4)=3(x + 2)\).
For the left - hand side, using the distributive property \(a-(b - c)=a - b + c\), we have \(5-(x - 4)=5 - x+4=9 - x\).
For the right - hand side, using the distributive property \(a(b + c)=ab+ac\), we have \(3(x + 2)=3x+6\).
So the equation becomes \(9 - x=3x + 6\).

Step2: Move the terms with x to one side

We add \(x\) to both sides of the equation \(9 - x=3x + 6\) to get \(9=3x+x + 6\), which simplifies to \(9 = 4x+6\).

Step3: Solve for x

We subtract 6 from both sides of the equation \(9 = 4x+6\). So \(9-6=4x\), which gives \(3 = 4x\).
Then we divide both sides by 4, and we get \(x=\frac{3}{4}=0.75\).

Answer:

\(0.75\)