Question

solving multi-step inequalities notes
solve -8x + 1 ≤ 17 and graph the solution
solve 2x - 18 < -4x + 6 and graph the solution
will -2 have an open or a closed circle?
closed
open
rewatch

Explanation:

Step1: Solve \(2x - 18 < -4x+6\)

Add \(4x\) to both sides: \(2x + 4x-18 < -4x + 4x+6\), so \(6x-18 < 6\).

Step2: Isolate the term with \(x\)

Add \(18\) to both sides: \(6x-18 + 18<6 + 18\), so \(6x<24\).

Step3: Solve for \(x\)

Divide both sides by \(6\): \(\frac{6x}{6}<\frac{24}{6}\), so \(x < 4\).

For the first inequality \(-8x + 1\leq17\), when we divide by \(- 8\) (a negative number), the inequality sign flips. The solution \(x\geq - 2\) has a closed circle because the inequality is \(\geq\) (includes the value \(-2\)).

Answer:

For \(2x - 18 < -4x + 6\), the solution is \(x < 4\). For the question about \(-2\) in \(x\geq - 2\), the answer is closed.