Question

solve for x.
5(x - 10) = 30 - 15x
\\(\circ\\) \\(x = 1\\)
\\(\circ\\) \\(x = 4\\)
\\(\circ\\) \\(x = 5\\)
\\(\circ\\) \\(x = 8\\)

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b - c)=ab - ac\), we have \(5(x - 10)=5x-50\). So the equation becomes \(5x - 50=30 - 15x\).

Step2: Add \(15x\) to both sides

Adding \(15x\) to both sides to get all \(x\) terms on one side: \(5x+15x - 50=30 - 15x+15x\), which simplifies to \(20x - 50=30\).

Step3: Add 50 to both sides

Adding 50 to both sides: \(20x - 50 + 50=30 + 50\), so \(20x=80\).

Step4: Divide by 20

Dividing both sides by 20: \(\frac{20x}{20}=\frac{80}{20}\), which gives \(x = 4\).

Answer:

\(x = 4\) (corresponding to the option \(x = 4\))