Question

and graph the solution on the number line below.
-3x < 27
attempt 2 out of 2
≤ ≥ or
lity notation: > -9
er line:
-10 -8 -6 -4 -2 0 2 4 6 8 10 12
click line to delete. click closed circle to change to open circle.
mit answer

Explanation:

Step1: Divide both sides by -3 (reverse inequality)

To solve \(-3x < 27\), divide both sides by \(-3\). Remember that when dividing an inequality by a negative number, the inequality sign flips. So we have:
\[
\frac{-3x}{-3} > \frac{27}{-3}
\]

Step2: Simplify both sides

Simplifying the left side, \(\frac{-3x}{-3} = x\). Simplifying the right side, \(\frac{27}{-3} = -9\). So the solution is:
\[
x > -9
\]

Answer:

The solution to the inequality \(-3x < 27\) is \(x > -9\). For the number line, we use an open circle at \(-9\) (since \(x\) is not equal to \(-9\)) and shade the region to the right of \(-9\) to represent all values of \(x\) greater than \(-9\).