# One-step inequalities review

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

## Inequalities symbols

SymbolMeaning
is greater thanGreater than
$\underline>$Greater than or equal to
is less thanLess than
$\underline<$Less 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 blueD, s, u, b, t, r, a, c, t, space, 7, end color blueD from both sides.
x, plus, 7, start color blueD, minus, 7, end color blueD, is greater than, 4, start color blueD, minus, 7, end color blueD
Now, we simplify.
x, is greater than, minus, 3
Example 2: $z-11\,\ \underline< \,\, 5$
To isolate z, let's start color greenD, a, d, d, space, 11, end color greenD to both sides.
$z-11\greenD{+11}\,\ \underline< \,\, 5\greenD{+11}$
Now, we simplify.
$z\,\ \underline< \,\,16$

### Practice set 1

Problem 1A
Solve for x.
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: $\dfrac{y}{-6}\,\ \underline>\,\ 4$
To isolate y, let's multiply both sides by minus, 6.
$\left(\dfrac{y}{-6}\right)\times-6\,\ \underline>\,\ 4\times-6$
Now, we simplify.
$y\,\ \underline<\,-24$
When we multiply or divide by a negative number, the inequality symbol becomes its opposite.
In other words, because we multiplied by negative 6 our $\underline>$ symbol became $\underline<$.

Problem 2A
Solve for x.