Using Technology to Visualize Inequality Solutions

2.9.6 Using Technology to Visualize Inequality Solutions

2.9.6 • Using Technology to Visualize Inequality Solutions

Activity

Consider the inequality $- \frac{1}{2} x + 6 < 4 x - 3$ . Let’s look at another way to find its solutions.

Use the graphing tool or technology outside the course. Graph $y = - \frac{1}{2} x + 6$ and $y = 4 x - 3$ on the same coordinate plane using the Desmos tool below.

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Compare your answer:

Graph showing two intersecting lines: a blue line with a positive slope and a black line with a gentle, negative slope, on an x-y coordinate plane.

Use your graphs to answer the following questions:

Find the values of $- \frac{1}{2} x + 6$ and $4 x - 3$ when $x$ is 1.

Compare your answer:

When $x$ is 1, find the value of $- \frac{1}{2} x + 6$ is $5 \frac{1}{2}$ , and the value of $4 x - 3$ is 1.

What value of $x$ makes $- \frac{1}{2} x + 6$ and $4 x - 3$ equal?

Compare your answer:

When $x$ is equal to 2, the value of $- \frac{1}{2} x + 6$ is equal to that of $4 x - 2$ .

For what values of $x$ is $- \frac{1}{2} x + 6$ less than $4 x - 3$ ?

Compare your answer:

When $x$ is greater than 2, the value of $- \frac{1}{2} x + 6$ is less than that of $4 x - 3$ .

For what values of $x$ is $- \frac{1}{2} x + 6$ greater than $4 x - 3$ ?

Compare your answer:

When $x$ is less than 2, the value of $- \frac{1}{2} x + 6$ is greater than that of $4 x - 3$ .

What is the solution to the inequality $- \frac{1}{2} x + 6 < 4 x - 3$ ? Be prepared to explain how you know.

Compare your answer: $x > 2$