solve the linear inequality for a. graph your answer in the number line. then write the solution in…

Explanation:

Step1: Combine like - terms on both sides

Combine the constant terms on the left - hand side: $-3-3=-6$, and combine the $a$ terms on the right - hand side: $6a - 4a = 2a$. The inequality becomes $-6-3a\geq - 1+2a$.

Step2: Move the variable terms to one side

Add $3a$ to both sides of the inequality: $-6-3a + 3a\geq - 1+2a+3a$, which simplifies to $-6\geq - 1 + 5a$.

Step3: Move the constant terms to one side

Add $1$ to both sides: $-6 + 1\geq - 1+1 + 5a$, resulting in $-5\geq5a$.

Step4: Solve for $a$

Divide both sides by $5$: $\frac{-5}{5}\geq\frac{5a}{5}$, so $-1\geq a$ or $a\leq - 1$.

To graph on the number line, draw a number line, mark a closed circle at $-1$ (because the inequality is $\leq$) and shade to the left of $-1$.

Answer:

$a\leq - 1$