Question

solve the following linear equation:
$2(-3s - 13) - 10s = -22s - 2$
enter each solution as an integer or reduced fraction only. decimal and mixed number answers will not be accepted. enter r if the solution is all real numbers. enter dne if there is no real solution.
$s = \square$

Explanation:

Step1: Expand the left side

First, we expand \(2(-3s - 13)\) using the distributive property \(a(b + c)=ab+ac\). So, \(2(-3s - 13)=2\times(-3s)+2\times(-13)= -6s - 26\). Then the left side of the equation becomes \(-6s - 26 - 10s\). Combining like terms \(-6s-10s=-16s\), so the left side is \(-16s - 26\). The equation now is \(-16s - 26=-22s - 2\).

Step2: Add \(22s\) to both sides

To get all the \(s\) terms on one side, we add \(22s\) to both sides. \(-16s+22s - 26=-22s+22s - 2\). Simplifying, \(6s - 26=-2\).

Step3: Add 26 to both sides

Now, we add 26 to both sides to isolate the term with \(s\). \(6s - 26 + 26=-2 + 26\). Simplifying, \(6s = 24\).

Step4: Divide both sides by 6

To solve for \(s\), we divide both sides by 6. \(\frac{6s}{6}=\frac{24}{6}\), which gives \(s = 4\).

Answer:

\(4\)