Question

solve the following linear equation:
$2\left(-3s - 13\
ight) - 10s = -22s - 2$
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 - hand side

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

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

Adding \(22s\) to both sides of the equation \(-16s-26=-22s - 2\) gives \(-16s + 22s-26=-22s+22s - 2\). Combining like terms, \(-16s + 22s = 6s\) and \(-22s+22s = 0\), so the equation becomes \(6s-26=-2\).

Step3: Add 26 to both sides

Adding 26 to both sides of \(6s-26=-2\) gives \(6s-26 + 26=-2 + 26\). Simplifying, we get \(6s=24\).

Step4: Divide both sides by 6

Dividing both sides of \(6s = 24\) by 6, we have \(\frac{6s}{6}=\frac{24}{6}\), which simplifies to \(s = 4\).

Answer:

\(s = 4\)