Question

solve the inequality and graph the solution on the line provided. -69 - 6x < -75
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
touch and drag to plot line

Explanation:

Step1: Add 69 to both sides

To isolate the term with \( x \), we add 69 to both sides of the inequality \(-69 - 6x < -75\). This gives us \(-69 - 6x + 69 < -75 + 69\), which simplifies to \(-6x < -6\).

Step2: Divide by -6 (reverse inequality)

When dividing both sides of an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \(-6x < -6\) by \(-6\) gives \(x > 1\) (since \(\frac{-6x}{-6} > \frac{-6}{-6}\)).

Answer:

Inequality Notation: \( x > 1 \)
(For the number line, we would draw an open circle at 1 and an arrow pointing to the right to represent all numbers greater than 1.)