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.)
