One-Step Inequalities Practice Test

Solve one-step inequalities and practice when the inequality sign must reverse.

One-Step Inequalities Practice Test

20 one-step inequality questions with sign reversals, graphs, applications, and worked explanations.

Instant feedback · Worked explanations

After the test · inequality signal system

A one-step inequality asks for one inverse operation — but the answer is a whole direction of values, not a single number

These problems are short enough that every symbol matters. You must identify the inverse operation, preserve or reverse the inequality direction when appropriate, decide whether the boundary is included, and read the final answer as a set.

Add / subtractMultiply / divideNegative coefficients Open endpointClosed endpointNumber-line direction

The special rule to remember: only multiplication or division by a negative number reverses the inequality sign.

Four signal types

The inequality symbol tells you whether the boundary is included and which comparison is being made

Less than

Boundary excluded. Use an open endpoint.

Greater than

Boundary excluded. Use an open endpoint.

≤

At most

Boundary included. Use a closed endpoint.

≥

At least

Boundary included. Use a closed endpoint.

x + 7 < 15

subtract 7

x < 8

x − 4 ≥ 9

add 4

x ≥ 13

5x ≤ 30

divide by 5

x ≤ 6

x/3 > 4

multiply by 3

x > 12

Negative-coefficient alert

When the one inverse step divides by a negative number, reverse the inequality immediately

Start

−4x ≥ 20

Divide by −4

x ≤ −5

Why flip?

Multiplying or dividing by a negative reverses numerical order.

Endpoint board

Open and closed endpoints encode whether equality is allowed

Strict inequality

x < 4 or x > 4

Use an open circle because the boundary value itself is excluded.

Inclusive inequality

x ≤ 4 or x ≥ 4

Use a closed circle because equality makes the boundary part of the solution set.

Direction strips

The final symbol tells you which side of the boundary belongs to the solution

x < 5

Shade toward smaller numbers.

x ≥ 5

Include 5 and shade toward larger numbers.

Signed-number checkpoint

Negative values can appear in the boundary, the coefficient, or both

Separate the arithmetic sign from the inequality-direction rule.

Negative boundary x + 3 < −2
→ x < −5

No sign reversal occurs because the inverse operation is subtraction.

Negative coefficient −2x < 10
→ x > −5

Divide by −2 and reverse the sign.

Negative divisor x/(−4) ≥ 3
→ x ≤ −12

Multiply by −4 and reverse the sign.

Fraction and decimal lane

Fractions and decimals do not change the one-step logic

Decimal coefficient

0.5x > 4 → x > 8

Divide by positive 0.5, so the sign stays the same.

Negative decimal

−0.25x ≤ 2 → x ≥ −8

Division by −0.25 reverses ≤ to ≥.

Fractional coefficient

(2/3)x < 6 → x < 9

Multiply by positive reciprocal 3/2; direction stays unchanged.

One-step limit model

Short inequality stories usually translate directly into a minimum or maximum

Maximum capacity

40 people

People already inside

Additional people

Inequality

x + 13 ≤ 40

Solution

x ≤ 27

Test-value pulse

One quick substitution can confirm that the direction of your answer makes sense

Solution:
x ≤ −5

→

Test x = −6
−4(−6)=24

→

24 ≥ 20
TRUE ✓

Signal error scan

Most one-step inequality errors come from one of four tiny symbol decisions

Forgot the flip

−3x > 9 → x > −3 x < −3

Dividing by −3 reverses the inequality.

Flipped unnecessarily

x − 5 < 2 → x > 7 x < 7

Adding 5 does not reverse the sign.

Wrong endpoint

x ≥ 4 shown with an open circle Use a closed circle.

The equality part means 4 belongs to the solution set.

Wrong direction

x < 4 shaded to the right Shade toward smaller values.

Numbers less than 4 lie to the left on a number line.

One-step signal diagnostics

Use missed questions to identify exactly which small rule needs reinforcement

Inverse operation The wrong one-step operation was chosen.

Sign reversal The inequality was or was not flipped at the correct moment.

Boundary type Open versus closed endpoint was misread.

Direction The solution was shaded or interpreted on the wrong side.