Question

solve the inequality and graph the solution.
6 ≤ 3(h − 2)
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
← -5 -4 -3 -2 -1 0 1 2 3 4 5 →
submit
work it out
not feeling ready yet? these can help:
graph solutions to one-step inequalities (75)
solve multi-step inequalities

Explanation:

Step1: Divide both sides by 3

To isolate the expression with \( h \), we divide both sides of the inequality \( 6 \leq 3(h - 2) \) by 3. Since 3 is positive, the direction of the inequality sign remains the same.
\[
\frac{6}{3} \leq \frac{3(h - 2)}{3}
\]
Simplifying both sides, we get:
\[
2 \leq h - 2
\]

Step2: Add 2 to both sides

To solve for \( h \), we add 2 to both sides of the inequality \( 2 \leq h - 2 \).
\[
2 + 2 \leq h - 2 + 2
\]
Simplifying both sides, we obtain:
\[
4 \leq h
\]
Which can also be written as \( h \geq 4 \).

To graph the solution:

• The endpoint is at \( h = 4 \). Since the inequality is "greater than or equal to", the endpoint is a closed circle (filled in).
• The arrow points to the right (towards positive infinity) because we are looking for all values of \( h \) that are greater than or equal to 4.

Answer:

The solution to the inequality \( 6 \leq 3(h - 2) \) is \( h \geq 4 \). To graph it, plot a closed circle at \( 4 \) on the number line and draw an arrow to the right.