Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Inequalities Practice Quiz: Test Your Skills

Master problems quickly with guided practice

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Inequalities Unlocked, an engaging algebra quiz for high school students.

Solve the inequality: 2x - 3 > 1.
x > 2
x < 2
x ≥ 2
x ≤ 2
First, add 3 to both sides to get 2x > 4, then divide by 2 to obtain x > 2. This straightforward process confirms the correct solution.
Solve the inequality: x + 5 ≤ 10.
x ≤ 5
x < 5
x ≥ 5
x > 5
Subtracting 5 from both sides yields x ≤ 5. This simple subtraction isolates the variable and confirms the correct answer.
Solve the inequality: 3x + 2 < 11.
x < 3
x ≤ 3
x > 3
x ≥ 3
Subtract 2 from both sides to get 3x < 9, then divide by 3 to find x < 3. This step-by-step isolation of x confirms the correct answer.
Express the solution of the inequality -4 < x ≤ 2 in interval notation.
(-4, 2]
[-4, 2]
(-4, 2)
[-4, 2)
The inequality indicates that x is greater than -4 but less than or equal to 2, which is represented as (-4, 2]. This notation clearly distinguishes between open and closed endpoints.
Which inequality correctly represents the phrase 'x is at least 7'?
x ≥ 7
x > 7
x ≤ 7
x < 7
The phrase 'at least' means the value can be equal to or greater than 7. Thus, x ≥ 7 is the correct representation.
Solve the inequality: -3x ≥ 9.
x ≤ -3
x ≥ -3
x < -3
x > -3
Dividing both sides by -3 requires flipping the inequality sign, yielding x ≤ -3. This critical step ensures the direction of the inequality is correct.
Solve the compound inequality: 1 < 2x + 1 ≤ 7.
0 < x ≤ 3
1 < x ≤ 7
0 ≤ x < 3
1 ≤ x < 7
Subtract 1 from every part to obtain 0 < 2x ≤ 6, then divide by 2 to find 0 < x ≤ 3. This methodical process correctly handles the compound nature of the inequality.
Solve the inequality: -2x + 5 > 1.
x < 2
x > 2
x ≤ 2
x ≥ 2
Subtract 5 from both sides to get -2x > -4, then divide by -2 and flip the inequality sign to obtain x < 2. The sign change when dividing by a negative is key.
Solve the inequality: 4 - 3x < 10.
x > -2
x < -2
x ≥ -2
x ≤ -2
Subtract 4 from both sides to get -3x < 6, then divide by -3 while flipping the inequality sign, resulting in x > -2. This demonstrates correct handling of negatives in inequalities.
Solve the inequality: (x/3) + 2 ≥ 5.
x ≥ 9
x < 9
x ≤ 9
x > 9
Subtract 2 from both sides to obtain x/3 ≥ 3, then multiply by 3 to isolate x, resulting in x ≥ 9. This procedure properly maintains the inequality direction as all operations are with positive numbers.
Solve the inequality: -5 + 2x ≤ 3x - 1.
x ≥ -4
x ≤ -4
x > -4
x < -4
Subtracting 2x from both sides gives -5 ≤ x - 1, and adding 1 results in -4 ≤ x, which is equivalent to x ≥ -4. This step-by-step rearrangement isolates x correctly.
Solve the inequality: 2(x - 1) > 3x - 4.
x < 2
x > 2
x ≥ 2
x ≤ 2
Expanding gives 2x - 2 > 3x - 4; subtracting 2x from both sides results in -2 > x - 4. Adding 4 to both sides yields 2 > x, which means x < 2. This systematic approach confirms the solution.
Solve the inequality: 3 - 2(x + 1) < x.
x > 1/3
x < 1/3
x ≤ 1/3
x ≥ 1/3
First, expand the left side to obtain 3 - 2x - 2, which simplifies to 1 - 2x < x. Adding 2x to both sides gives 1 < 3x, and dividing by 3 yields x > 1/3. This confirms the correct redistribution of terms.
Solve the inequality: -4(x - 1) ≤ 8.
x ≥ -1
x ≤ -1
x > -1
x < -1
Expanding gives -4x + 4 ≤ 8. Subtracting 4 from both sides yields -4x ≤ 4, and dividing by -4 (remember to flip the inequality) results in x ≥ -1. The division step is key to getting the correct answer.
Solve the inequality: x/2 < 3.
x < 6
x > 6
x ≤ 6
x ≥ 6
Multiplying both sides by 2 isolates x, giving x < 6. This clear multiplication step confirms the correct solution.
Solve the quadratic inequality: 2x² - 5x + 2 < 0.
1/2 < x < 2
x < 1/2 or x > 2
x > 2
x ≤ 1/2 or x ≥ 2
Factoring the quadratic gives (2x - 1)(x - 2) < 0. Analyzing the sign changes shows the expression is negative for values between the roots, hence 1/2 < x < 2.
Solve the absolute value inequality: |2x - 3| > 5.
x < -1 or x > 4
-1 ≤ x ≤ 4
-1 < x < 4
x > -1 and x < 4
The inequality splits into 2x - 3 > 5 or 2x - 3 < -5. Solving these gives x > 4 or x < -1. Combining these results confirms the solution is x < -1 or x > 4.
Solve the rational inequality: (x - 2)/(x + 1) ≥ 0.
(-∞, -1) ∪ [2, ∞)
(-∞, -1] ∪ (2, ∞)
(-∞, -1) ∪ (2, ∞)
[-1, 2]
Identify the critical points x = 2 (zero of the numerator) and x = -1 (undefined point). Testing intervals shows the expression is nonnegative for x in (-∞, -1) and for x ≥ 2, with x = -1 excluded.
Solve the absolute value inequality: |x + 4| ≤ 3.
-7 ≤ x ≤ -1
-3 ≤ x ≤ 3
-1 ≤ x ≤ 7
x < -7 or x > -1
Rewriting the inequality as -3 ≤ x + 4 ≤ 3 and then subtracting 4 from all parts yields -7 ≤ x ≤ -1. This compound inequality approach correctly bounds the value of x.
Solve the inequality: (x - 1)/(x + 2) < 0.
-2 < x < 1
x < -2 or x > 1
-2 ≤ x ≤ 1
-2 < x ≤ 1
Determine the critical values x = 1 and x = -2, then test intervals. The inequality holds when the numerator and denominator have opposite signs, which occurs for -2 < x < 1, excluding x = -2 as it makes the denominator zero.
0
{"name":"Solve the inequality: 2x - 3 > 1.", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Solve the inequality: 2x - 3 > 1., Solve the inequality: x + 5 ≤ 10., Solve the inequality: 3x + 2 < 11.","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand and interpret the meaning of inequality symbols.
  2. Analyze algebraic expressions to determine correct inequality solutions.
  3. Apply methods for isolating variables when solving linear inequalities.
  4. Evaluate problem-solving strategies to choose the most efficient approach.
  5. Demonstrate accuracy in verifying solutions to inequality problems.

1.06 Inequalities Quiz: Practice Test Cheat Sheet

  1. Understand the symbols - Think of "<" and ">" as tiny alligators chomping on the bigger number, while "≤" and "≥" let the gator chill if the numbers are equal - super handy for reading inequalities fast. Swap them for "less than," "greater than," "less than or equal to," and "greater than or equal to" in your head to stay on top of the game! SparkNotes: Algebra 1 Inequalities
    2. SparkNotes: Algebra 1 Inequalities
  2. Keep the sign steady with addition/subtraction - If you add or subtract the same number on both sides, the inequality sign stays loyal and doesn't change direction. It's like keeping balance on a seesaw - as long as the weight shift is equal, things remain fair! CourseSidekick: Mathematics Inequality Rules
    3. CourseSidekick: Mathematics Inequality Rules
  3. Flip it when you multiply/divide by negatives - Multiplying or dividing both sides by a negative number is like doing a 180° spin on your inequality arrow - don't forget to flip "<" to ">" or "≤" to "≥"! This little trick can save you from messy mistakes and keep your answers correct. SchoolTube: Conquering Inequalities in Algebra
    4. SchoolTube: Conquering Inequalities in Algebra
  4. Gather like terms - When variables appear on both sides, play detective and move all x‑terms to one side and constants to the other. This makes solving a breeze, like organizing your desk before you start homework! NeuroChispas: Examples of Inequalities
    5. NeuroChispas: Examples of Inequalities
  5. Graph it out - Draw your solutions on a number line, using an open circle for "<" or ">" and a closed circle for "≤" or "≥." This visual hack helps you see exactly where your answers live and avoids any fuzzy mistakes. SparkNotes: Algebra 1 Inequalities
    6. SparkNotes: Algebra 1 Inequalities
  6. Crack compound inequalities - Tackle each side of an "and" or "or" separately, then combine them like puzzle pieces: intersect for "and" or unite for "or." It's like juggling two routines at once, but once you get the flow, it's super satisfying! MathWorksheets4Kids: Inequalities Worksheet
    7. MathWorksheets4Kids: Inequalities Worksheet
  7. Master absolute value cases - For |expression|, split into positive and negative cases and solve each inequality separately. Think of it as facing both sides of the coin - you won't miss any solutions! MathWorksheets4Kids: Inequalities Worksheet
    8. MathWorksheets4Kids: Inequalities Worksheet
  8. Double-check your work - Plug your solution back into the original inequality to make sure it actually makes the statement true. It's like using spell-check for math - catch those sneaky errors early! Third Space Learning: Solving Inequalities Guide
    9. Third Space Learning: Solving Inequalities Guide
  9. Mix up your practice - Solve one-step, two-step, and multi-step inequalities to level up your skills and confidence. The more flavors you taste, the more fearless you'll feel tackling any problem! MathGeekMama: Solve Inequalities Practice
    10. MathGeekMama: Solve Inequalities Practice
  10. Express your final range - Inequalities give you a whole playground of answers, so choose interval notation or graph form to show where your solutions hang out. Think of interval notation as a secret code that concisely sums up your solution set. BYJU'S: Solving Inequalities Worksheets
    11. BYJU'S: Solving Inequalities Worksheets
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker