Question

solve the inequality and graph the solution.
7(f - 2) - 4 ≤ 10
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
number line with -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
submit

Explanation:

Step1: Expand the left side

First, we expand \(7(f - 2)\) using the distributive property \(a(b - c)=ab - ac\). So \(7(f - 2)=7f-14\). Then the inequality becomes \(7f - 14-4\leq10\).

Step2: Simplify the left side

Combine like terms on the left side. \(- 14-4=-18\), so the inequality is \(7f-18\leq10\).

Step3: Add 18 to both sides

To isolate the term with \(f\), we add 18 to both sides of the inequality. \(7f-18 + 18\leq10 + 18\), which simplifies to \(7f\leq28\).

Step4: Divide both sides by 7

Divide both sides of the inequality \(7f\leq28\) by 7. \(\frac{7f}{7}\leq\frac{28}{7}\), so \(f\leq4\).

To graph the solution: We draw a number line. We plot a closed circle at \(f = 4\) (because the inequality is \(\leq\), so 4 is included in the solution set) and draw a ray pointing to the left (towards negative infinity) to represent all numbers less than or equal to 4.

Answer:

The solution to the inequality is \(f\leq4\). The graph has a closed circle at 4 and a ray extending to the left from 4.