Describing Steps in solving a Linear Inequality

Name:__________________ Describing Steps in solving a Linear Inequality

Below you will find the completed steps to a problem with directions “Solve the linear inequality, show the

solution on a number line, and write the solution in interval notation.” Write a description of what happened in

each step and answer the questions.

Solve the linear inequality 1. 4(𝑥 − 3) < 2 − 3(3𝑥 − 4)

2. 4𝑥 − 12 < 2 − 9𝑥 + 12

3. 4𝑥 − 12 < −9𝑥 + 14

4. 13𝑥 − 12 < 14

5. 13𝑥 < 26

6. 𝑥 < 2

a) From step one to step two:

b) From step two to step three:

c) From step three to step four:

d) From step four to step five:

e) From step five to step six:

Number line solution Step one: place a ( or a [.

f) A parenthesis was placed on the line, is this correct? Why or why not?

Step two: shade

g) The line was shaded to the left, is this

correct? Why or why not?

Interval notation 𝐴. (−∞, 2], 𝐵. (−∞, 2)

𝐶. [2, ∞) 𝐷. (2, ∞)

h) Which is the correct interval notation and why? (Describe each parenthesis and/or bracket and infinity in your explanation.)