Question

solve the linear inequality for x. graph your answer in the number line. then write the solution in inequality notation.
-12x + 20x > 2(8x - 9) + 10
show your work here
hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

Explanation:

Step1: Simplify both sides

Simplify left - hand side: \(-12x + 20x=8x\).
Simplify right - hand side: \(2(8x - 9)+10=16x-18 + 10=16x - 8\).
The inequality becomes \(8x>16x - 8\).

Step2: Move terms with \(x\) to one side

Subtract \(16x\) from both sides: \(8x-16x>16x - 8-16x\).
\(-8x>-8\).

Step3: Solve for \(x\)

Divide both sides by \(-8\). When dividing an inequality by a negative number, the inequality sign flips. So \(\frac{-8x}{-8}<\frac{-8}{-8}\).
\(x < 1\).

Answer:

The solution in inequality notation is \(x < 1\). On the number line, we have an open circle at \(x = 1\) (because \(x\) is not equal to \(1\)) and the line extends to the left of \(1\).