Question

solve the inequality and graph the solution.
a - 4 ≤ 3
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.

Explanation:

Step1: Isolate the variable \(a\)

Add \(4\) to both sides of the inequality \(a - 4\leq3\).
Using the addition property of inequalities: \(a-4 + 4\leq3 + 4\).

Step2: Simplify

Simplify the left - hand side \(a-4 + 4=a\) and the right - hand side \(3 + 4 = 7\). So, \(a\leq7\).

To graph \(a\leq7\) on the number line:

• Place a closed circle at \(7\) (because the inequality is \(\leq\), which includes the endpoint).
• Draw a ray to the left of \(7\) (since \(a\) can be any number less than or equal to \(7\)).

Answer:

The solution of the inequality \(a - 4\leq3\) is \(a\leq7\). On the number line, there is a closed circle at \(7\) and a ray extending to the left.