Question

solve the inequality and graph the solution.
\\(\frac{q}{2} - 1 \leq 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.
(number line from -10 to 10 with ticks at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10)

Explanation:

Step1: Add 1 to both sides

To isolate the term with \( q \), we add 1 to both sides of the inequality \(\frac{q}{2}-1\leq2\). This gives us \(\frac{q}{2}-1 + 1\leq2 + 1\), which simplifies to \(\frac{q}{2}\leq3\).

Step2: Multiply both sides by 2

To solve for \( q \), we multiply both sides of the inequality \(\frac{q}{2}\leq3\) by 2. This gives us \(\frac{q}{2}\times2\leq3\times2\), which simplifies to \(q\leq6\).

Answer:

The solution to the inequality is \( q\leq6 \). To graph this, we plot a closed endpoint at 6 on the number line and draw an arrow to the left (towards negative infinity) to represent all values of \( q \) less than or equal to 6.