Question

Graph the inequality. \(-10 \leq-x\)

Short answer

The graph should have a filled point at 10 and the line should extend to the left, representing all the numbers which are less than or equal to 10.

Step-by-step solution

Simplify the Inequality

First, -x should be transformed into a positive form. That can be achieved by multiplying both sides of the inequality by -1. However, when multiplying or dividing both sides of an inequality by a negative number, the inequality symbol must be reversed. The simplified inequality now is \(x \leq 10\).

Identify the Number Line

The inequality represents a collection of numbers which are less than or equal to 10. These values will be represented on the number line. Hence, every value to the left of 10, including 10, will be included in the solution of the inequality.

Graph the Inequality

Plot the point at x = 10 and fill the dot since the solution includes 10 (as indicated by the \(\leq\)). Draw a line to the left of 10, indicating all numbers less than 10 are part of the solution.