Question

Solve the inequality and graph its solution. \(-2 b \leq-8\)

Short answer

The solution to the inequality is \(b \geq 4\).

Step-by-step solution

Understand and Rewrite the Inequality

The given inequality is \(-2b \leq-8\). This inequality means \(-2b\) is less than or equals to \(-8\). Our goal is to isolate \(b\). In order to do this, it is necessary to divide by \(-2\).

Divide by Negative Coefficient

Divide each side of the inequality by \(-2\) to isolate \(b\). Here we must remember an important rule: When you multiply or divide an inequality by a negative number, you must reverse the inequality symbol. Hence we get, \(b \geq 4\).

Represent the Solution Graphically

To graph this on a number line, place a filled circle on \(4\) (because \(4\) is included in the solution) and draw a line extending to the right from \(4\) (since it includes all numbers greater than \(4\)).