Question

solve the inequality and graph the solution. 1 ≤ -5 + 3q to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it 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:

Explanation:

Step1: Subtract 5 from both sides

To isolate the term with \( q \), we subtract 5 from both sides of the inequality \( 1\leq5 + 3q \). This gives us \( 1-5\leq5 + 3q-5 \), which simplifies to \( - 4\leq3q \).

Step2: Divide both sides by 3

Now, we divide both sides of the inequality \( -4\leq3q \) by 3 to solve for \( q \). So we have \( \frac{-4}{3}\leq\frac{3q}{3} \), which simplifies to \( -\frac{4}{3}\leq q \) or \( q\geq-\frac{4}{3} \) (since \( -\frac{4}{3}\approx - 1.33\)).

To graph the solution:

• The endpoint is at \( q = -\frac{4}{3}\) (or approximately - 1.33). 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 \( q \) that are greater than or equal to \( -\frac{4}{3} \).

Answer:

The solution to the inequality \( 1\leq5 + 3q \) is \( q\geq-\frac{4}{3} \). For the graph, plot a closed circle at \( -\frac{4}{3} \) (or approximately - 1.33) on the number line and draw an arrow pointing to the right.