Question

show what you know
graph the solutions to $-3 > -2x + 9$.
$-3 > -2x + 9$

Explanation:

Step1: Subtract 9 from both sides

To isolate the term with \( x \), we subtract 9 from both sides of the inequality \( -3 > -2x + 9 \).
\[
-3 - 9 > -2x + 9 - 9
\]
\[
-12 > -2x
\]

Step2: Divide by -2 (reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. Divide both sides by -2.
\[
\frac{-12}{-2} < \frac{-2x}{-2}
\]
\[
6 < x
\]
Which is equivalent to \( x > 6 \).

To graph this, we draw an open circle at 6 (since \( x > 6 \) does not include 6) and shade the line to the right of 6 on the number line.

Answer:

The solution to the inequality \( -3 > -2x + 9 \) is \( x > 6 \). The graph should have an open circle at 6 and shading to the right of 6 on the number line.