Question

How do you solve and graph `x-3>7`?

Answer 1

Express the inequality as an equation, then test points to determine where to shade the graph.

Explanation:

Strategy: Express the inequality as an equation (i.e., with an equals sign). Graph the equation. Strict inequality lines are drawn as a dashed line. Shade the side of the line where the inequality is true.

Step 1. Express the inequality as an equation.

`x-3=7`
`x=10`

Step 2. Graph the equation. Because `>` is a strict inequality, the line should be drawn as dashed.

Step 3. Shade the side of the line where the inequality is true.

Trying `(0,0)` makes the given inequality `x-3>7` FALSE.

`x-3>7`
`0-3>7`
`-3>7` is FALSE, because `-3` is not greater than `7`

So don't shade that side of the line. However, trying the point `(12,0)` makes the given inequality TRUE.

`x-3>7`
`12-3>7`
`9>7` is TRUE, because `9` is indeed greater than `7`. So go ahead and shade the right side of the line.