Question

solve the linear inequality for x. graph your answer in the number line. then write the solution in inequality notation.
-3 + 17x - 5 - 12x < 13x

Explanation:

Step1: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side of the inequality.
$(-3 - 5)+(17x-12x)<13x$
$-8 + 5x<13x$

Step2: Move the $x$ terms to one side

Subtract $5x$ from both sides of the inequality.
$-8+5x - 5x<13x - 5x$
$-8 < 8x$

Step3: Solve for $x$

Divide both sides of the inequality by 8.
$\frac{-8}{8}<\frac{8x}{8}$
$-1 < x$

To graph on the number line: Draw an open circle at - 1 (because the inequality is $<$ and not $\leq$) and shade to the right of - 1.

The solution in inequality notation is $x>-1$.

Answer:

The solution of the inequality is $x > - 1$. On the number line, there is an open circle at - 1 and shading to the right.