Question

-53 < 9x + 1 < -26
click and drag the dots to graph the end points. the graph with the open circle on one end and closed circle on the other end can be switched around.
move both endpoints onto the number line
(click and drag down)
number line with -10, -5, -3, -1, 0, 1, 5, 10 and draggable points

Explanation:

Step1: Subtract 1 from all parts

To isolate the term with \( x \), we subtract 1 from each part of the inequality. So we have:
\( -53 - 1 < 9x + 1 - 1 < -26 - 1 \)
Simplifying each part:
\( -54 < 9x < -27 \)

Step2: Divide all parts by 9

To solve for \( x \), we divide each part of the inequality by 9. So:
\( \frac{-54}{9} < \frac{9x}{9} < \frac{-27}{9} \)
Simplifying each fraction:
\( -6 < x < -3 \)

Answer:

The solution to the inequality \( -53 < 9x + 1 < -26 \) is \( -6 < x < -3 \). For graphing, the left endpoint (open circle) is at \( -6 \) and the right endpoint (open circle) is at \( -3 \) on the number line.