Question

solve each equation. check your solution.

1. - 2a - 9 = 6a + 15

2.

Explanation:

Step1: Combine like - terms

Add \(2a\) to both sides of the equation \(-2a - 9=6a + 15\). We get \(-2a+2a - 9=6a+2a + 15\), which simplifies to \(-9 = 8a+15\).

Step2: Isolate the term with the variable

Subtract 15 from both sides: \(-9-15=8a+15 - 15\), so \(-24 = 8a\).

Step3: Solve for \(a\)

Divide both sides by 8: \(\frac{-24}{8}=a\), so \(a=-3\).

Step4: Check the solution

Substitute \(a = - 3\) into the original equation.
Left - hand side: \(-2(-3)-9=6 - 9=-3\).
Right - hand side: \(6(-3)+15=-18 + 15=-3\).
Since the left - hand side equals the right - hand side, \(a=-3\) is the correct solution.

Answer:

\(a=-3\)