Algebra 1 : How to graph a two-step inequality

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : How To Graph A Two Step Inequality

Which graph depicts the following inequality?

\(\displaystyle x\geq4y+12\)

Possible Answers:

Question_12_incorrect_2

Question_12_correct

No real solution.

Question_12_incorrect_3

Question_12_incorrect_1

Correct answer:

Question_12_correct

Explanation:

Let's put the inequality in slope-intercept form to make it easier to graph:

\(\displaystyle x\geq4y+12\)

\(\displaystyle x-12\geq4y+12-12\)

\(\displaystyle x-12\geq4y\)

\(\displaystyle \frac{x-12}{4}\geq\frac{4y}{y}\)

\(\displaystyle \frac{1}{4}x-3\geq y\)

The inequality is now in slope-intercept form. Graph a line with slope \(\displaystyle \frac{1}{4}\) and y-intercept \(\displaystyle -3\).

Because the inequality sign is greater than or equal to, a solid line should be used.

Next, test a point. The origin \(\displaystyle (0,0)\) is good choice. Determine if the following statement is true:

\(\displaystyle \frac{1}{4}(0)-3\geq0\)

The statement is false. Therefore, the section of the graph that does not contain the origin should be shaded.

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