Inequalities — Pre-Algebra Unit 7 practice.
This unit covers writing inequalities, solving inequalities and graphing inequalities — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers writing inequalities, solving inequalities and graphing inequalities — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Writing Inequalities
Students must be able to translate verbal phrases into inequality symbols (<, >, ≤, ≥) and write inequalities from real-world situations. Knowing which phrases map to which symbols is essential, as exam questions frequently use words like 'at least,' 'no more than,' 'fewer than,' and 'exceeds.' Students must also identify whether a situation requires a strict or non-strict inequality.
Key Points
- 'At least' and 'no less than' mean ≥; 'at most' and 'no more than' mean ≤
- 'Greater than' means >; 'less than' means <; neither includes the boundary value
- Real-world constraints (age limits, speed limits, budgets) almost always use ≤ or ≥
- The variable can appear on either side; flip the inequality symbol if you switch sides
A roller coaster requires riders to be at least 48 inches tall. Write an inequality for h, a rider's height.
'At least 48 inches' means 48 inches is allowed, so the symbol is ≥. Writing with the variable first gives h ≥ 48. This means any height equal to or greater than 48 is acceptable.
2 Solving Inequalities
Solving an inequality follows the same steps as solving an equation, with one critical difference: when you multiply or divide both sides by a negative number, you must reverse the inequality symbol. Exams test this rule directly, often by including a negative coefficient specifically to see if students flip the symbol. The solution is expressed as an inequality, not a single value.
Key Points
- Use inverse operations to isolate the variable, just like solving equations
- Multiplying or dividing by a negative number reverses the inequality symbol
- Adding or subtracting (positive or negative) does NOT change the symbol
- Check your answer by substituting a value from your solution set back into the original inequality
Solve: -3x + 5 > 14
First subtract 5 from both sides: -3x > 9. Then divide both sides by -3; because you are dividing by a negative, reverse the symbol: x < -3. The solution is all numbers less than -3.
3 Graphing Inequalities
Inequalities are graphed on a number line using a circle (open or closed) at the boundary value and an arrow showing the direction of all solutions. An open circle means the boundary value is NOT included (< or >); a closed circle means it IS included (≤ or ≥). Exams require students to both read an existing graph and draw a graph from a given inequality.
Key Points
- Open circle ( ○ ) → strict inequality (< or >); closed circle ( ● ) → non-strict inequality (≤ or ≥)
- Arrow pointing left = solutions decrease without bound; arrow pointing right = solutions increase without bound
- The circle is always placed at the boundary value (the number in the inequality)
- Match the direction of the arrow to the inequality symbol after the variable is isolated on the left
Graph the solution to x ≤ -2 on a number line.
The boundary value is -2, and the symbol ≤ includes -2, so draw a closed circle at -2. Because x must be less than or equal to -2, draw an arrow pointing to the left from -2. Every point on the arrow and at -2 is part of the solution set.
Questions, answered.
What is Inequalities?
Inequalities is Unit 7 of Pre-Algebra, covering writing inequalities, solving inequalities and graphing inequalities.
How to study for Pre-Algebra Unit 7?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.