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One-step inequalities review

Review evaluating one-step inequalities, and try some practice problems.

Inequalities symbols

SymbolMeaning
is greater thanGreater than
start underline, is greater than, end underlineGreater than or equal to
is less thanLess than
start underline, is less than, end underlineLess than or equal to

Evaluating inequalities with addition and subtraction

We evaluate inequalities like we evaluate equations: we want to isolate the variable.
Example 1: x, plus, 7, is greater than, 4
To isolate x, let's start color #11accd, start text, s, u, b, t, r, a, c, t, space, end text, 7, end color #11accd from both sides.
x, plus, 7, start color #11accd, minus, 7, end color #11accd, is greater than, 4, start color #11accd, minus, 7, end color #11accd
Now, we simplify.
x, is greater than, minus, 3
Example 2: z, minus, 11, space, start underline, is less than, end underline, 5
To isolate z, let's start color #1fab54, start text, a, d, d, space, end text, 11, end color #1fab54 to both sides.
z, minus, 11, start color #1fab54, plus, 11, end color #1fab54, space, start underline, is less than, end underline, 5, start color #1fab54, plus, 11, end color #1fab54
Now, we simplify.
z, space, start underline, is less than, end underline, 16
Want to learn more about one-step inequalities? Check out this video.

Practice set 1

Problem 1A
Solve for x.
Your answer must be simplified.
x, minus, 8, is less than, minus, 1

Evaluating inequalities with multiplication and division

Again, we want to isolate the variable. But things will get a little different when multiply or divide by a negative number. Look carefully to see what happens!
Example 1: 10, x, is less than, minus, 3
To isolate x, let's divide both sides by 10.
start fraction, 10, x, divided by, 10, end fraction, is less than, start fraction, minus, 3, divided by, 10, end fraction
Now, we simplify.
x, is less than, minus, start fraction, 3, divided by, 10, end fraction
Example 2: start fraction, y, divided by, minus, 6, end fraction, space, start underline, is greater than, end underline, space, 4
To isolate y, let's multiply both sides by minus, 6.
left parenthesis, start fraction, y, divided by, minus, 6, end fraction, right parenthesis, times, minus, 6, space, start underline, is greater than, end underline, space, 4, times, minus, 6
Now, we simplify.
y, space, start underline, is less than, end underline, minus, 24

Practice set 2

Problem 2A
Solve for x.
Your answer must be simplified.
2, x, is less than, 15

Want to try more problems like this? Check out this exercise.

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