Question

6(2r - 2) = -8r + 40

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b - c)=ab - ac\), we have \(6(2r - 2)=6\times2r-6\times2 = 12r-12\). So the equation becomes \(12r - 12=-8r + 40\).

Step2: Add \(8r\) to both sides

To get all the \(r\) terms on one side, we add \(8r\) to both sides: \(12r+8r - 12=-8r + 8r+ 40\), which simplifies to \(20r-12 = 40\).

Step3: Add 12 to both sides

To isolate the term with \(r\), we add 12 to both sides: \(20r-12 + 12=40 + 12\), so \(20r=52\).

Step4: Divide both sides by 20

To solve for \(r\), we divide both sides by 20: \(r=\frac{52}{20}\), and simplifying the fraction gives \(r=\frac{13}{5}=2.6\).

Answer:

\(r = \frac{13}{5}\) (or \(r = 2.6\))