Question
Which graph represents the solution to the inequality? -2.2(x - 8) more than or equal to 66?
Answers
GPT-4o mini
To determine which graph represents the solution to the inequality \(-2.2(x - 8) \geq 66\), we first need to solve the inequality.
1. Distribute the \(-2.2\):
\[
-2.2x + 17.6 \geq 66
\]
2. Subtract \(17.6\) from both sides:
\[
-2.2x \geq 66 - 17.6
\]
\[
-2.2x \geq 48.4
\]
3. Divide both sides by \(-2.2\) (remember to flip the inequality sign when dividing by a negative number):
\[
x \leq \frac{48.4}{-2.2}
\]
\[
x \leq -22
\]
The solution to the inequality is \(x \leq -22\).
On a number line graph, this would be represented by a closed circle (to denote that -22 is included in the solution) at -22 and shading to the left, indicating all values less than -22.
You can select the corresponding graph based on this description.
1. Distribute the \(-2.2\):
\[
-2.2x + 17.6 \geq 66
\]
2. Subtract \(17.6\) from both sides:
\[
-2.2x \geq 66 - 17.6
\]
\[
-2.2x \geq 48.4
\]
3. Divide both sides by \(-2.2\) (remember to flip the inequality sign when dividing by a negative number):
\[
x \leq \frac{48.4}{-2.2}
\]
\[
x \leq -22
\]
The solution to the inequality is \(x \leq -22\).
On a number line graph, this would be represented by a closed circle (to denote that -22 is included in the solution) at -22 and shading to the left, indicating all values less than -22.
You can select the corresponding graph based on this description.