Inequalities & Absolute Value Worksheets

What this worksheet covers

An inequalities handout puts a rule, a range of answers and a number line on one side of A4. Items are built as you ask for them, so a second run at the same level brings a fresh set rather than the same page again.

What lands on the page:

• solve x + 6 < 11
• solve 4x ≥ 32
• solve −3x ≤ 12
• solve 2x − 7 > 9
• solve 1 < x + 4 ≤ 9
• solve −5x + 2 > 17
• draw the answer on a number line

Choosing a level

Line diagrams matter here because each answer is shown on a number line. The rung sets whether a solve takes one step, two, or a reversal after dividing by a negative. Warm-Up keeps to a single move such as taking a constant from both sides. Practice puts a coefficient in front of the letter, and Steady brings the reversal that arrives with a negative divisor. Challenge sets a two-step chain where the order of the moves matters, and Mastery hands over a compound statement or one that ends below zero.

Counts sit between 3 and 15 for the whole sheet. Same difficulty holds every item on the rung that is showing. Mixed difficulties works down the list from that rung, so a group starting at Practice meets Practice, Steady, Challenge and Mastery in turn.

Write-in makes the working visible, and the flip is the step worth seeing. Multiple choice A–D checks faster at the start of a lesson, though choosing between x > 8 and x < 8 by eye hides whether any division happened at all.

A worked example

Two items, one routine and one that the marking notes keep finding.

Solve −3x ≤ 12. Divide both sides by −3. The numbers give 12 ÷ (−3) = −4, and dividing by a negative turns the symbol round: x ≥ −4. On a number line that is a filled dot at −4 with the arrow heading right.

Solve 2x − 7 > 9. Add 7 to both sides: 2x > 16. Halve them: x > 8. Here the dot at 8 stays open, because 8 itself does not satisfy the statement.

Marking with the answer key

A missed sign reversal explains the error in most of the examples below.

• −3x ≤ 12 answered x ≤ −4. The symbol survived a division by a negative untouched. It has to turn over: x ≥ −4.
• 2x − 7 > 9 answered 2x > 2. Seven was taken off instead of put on. Both sides gain 7, so 2x > 16, and the answer is x > 8.
• 1 < x + 4 ≤ 9 answered 5 < x ≤ 13. The outer numbers gained 4 while the middle lost it. Apply the same subtraction to all three parts: −3 < x ≤ 5.
• 4x ≥ 32 answered x ≥ 128. The 4 was multiplied rather than shared out. Thirty-two split four ways gives x ≥ 8.

Printing and using it

Print a number line beside each prompt, since the endpoint and shaded direction form part of the answer. Leave room on the pupil copy for the arrow and the two boundary marks; a line printed only in the key cannot help while solving.

Standard gives one item per line with room for two moves of working. Large-print widens the spacing for a younger group, and Compact holds a dozen items on a single side, which covers a starter. The Name / Date / Class header can be switched on, and the title can be renamed, so a set reads "Solving by a negative" instead of the topic name.

Dyslexia-friendly type widens spacing, which can help the minus sign in −4 stand apart from 4. Stretch lifts every third item a rung higher, but only on a page fixed at one level; use it once the class can handle the reversal.

One classroom habit: hand the compound questions to pairs, with one member reading the statement aloud and the other marking both ends on the line before anyone divides.

Keep going

Take the same arguments to the inequalities practice ladder, where each answer is marked at once, read the inequalities lesson for the number-line picture, or print linear equation worksheets, which keep the equals sign and drop the reversal.

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