Question

solve the inequality and graph the solution.

( k - 5 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.

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Explanation:

Step1: Isolate the variable \(k\)

Add \(5\) to both sides of the inequality \(k - 5\leq2\).
Using the addition property of inequalities: \(k-5 + 5\leq2 + 5\).

Step2: Simplify

Simplify both sides. On the left - hand side, \(k-5 + 5=k\), and on the right - hand side, \(2 + 5 = 7\). So the solution of the inequality is \(k\leq7\).

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

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

Answer:

The solution of the inequality \(k - 5\leq2\) is \(k\leq7\). On the number line, there is a closed circle at \(7\) and a ray extending to the left.