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Quizzes > High School Quizzes > Mathematics

Two Step Inequalities Quiz: Practice PDF Worksheet

Sharpen your skills with interactive practice exercises

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Interactive quiz art for Master Two-Step Inequalities practice, challenging middle and high school students.

Solve the inequality: x + 4 > 10
x > 6
x > 14
x > -6
x > 10
Subtracting 4 from both sides yields x > 6. This step correctly isolates the variable.
Solve the inequality: 3x - 5 < 10
x < 5
x < 15
x > 5
x > 15
Adding 5 to both sides gives 3x < 15, then dividing by 3 results in x < 5. Thus, x < 5 is the correct result.
Solve the inequality: 2x + 7 ≥ 11
x ≥ 2
x > 2
x ≥ 4
x > 4
Subtract 7 from both sides to get 2x ≥ 4, then divide by 2 to isolate x and find x ≥ 2. So, x ≥ 2 is correct.
Solve the inequality: 5 - x ≤ 2
x ≤ 3
x ≥ 3
x < 3
x > 3
Subtracting 5 from both sides yields -x ≤ -3 and multiplying by -1 (which reverses the inequality) gives x ≥ 3. Therefore, x ≥ 3 is the correct answer.
Solve the inequality: 4x - 3 > 5
x > 2
x ≥ 2
x > 8
x < 2
Adding 3 to both sides results in 4x > 8, and dividing by 4 gives x > 2. Hence, x > 2 is the correct solution.
Solve the inequality: -2x + 3 > 7
x < -2
x > -2
x < 2
x > 2
Subtracting 3 yields -2x > 4; dividing by -2 reverses the inequality sign to give x < -2. This is the correct method to solve the inequality.
Solve the inequality: 3 - 5x ≥ 13
x ≥ -2
x ≤ -2
x < -2
x > -2
Subtracting 3 gives -5x ≥ 10; dividing by -5 (and reversing the inequality) results in x ≤ -2. Hence, x ≤ -2 is correct.
Solve the inequality: -3x - 4 < 2
x < -2
x > -2
x < 2
x > 2
Adding 4 to both sides yields -3x < 6; dividing by -3 (with inequality reversal) gives x > -2. Thus, x > -2 is the correct answer.
Solve the inequality: 7 - 2x ≤ 3
x ≤ 2
x ≥ 2
x > 2
x < 2
Subtracting 7 yields -2x ≤ -4; dividing by -2 (remember to flip the inequality) results in x ≥ 2. Therefore, x ≥ 2 is correct.
Solve the inequality: 4 - 3x > 1
x > 1
x < 1
x ≥ 1
x ≤ 1
Subtracting 4 yields -3x > -3; dividing by -3 (and reversing the inequality) gives x < 1. Therefore, x < 1 is correct.
Solve the inequality: 2(x - 1) < 6
x < 4
x ≤ 4
x > 4
x ≥ 4
First distribute to get 2x - 2 < 6, then isolate x by adding 2 and dividing by 2, resulting in x < 4. Thus, x < 4 is the correct solution.
Solve the inequality: -4(2x + 3) ≥ 8
x ≥ -5/2
x ≤ -5/2
x > -5/2
x < -5/2
Distribute -4 to obtain -8x - 12 ≥ 8; adding 12 results in -8x ≥ 20, and dividing by -8 (with sign reversal) yields x ≤ -5/2. That is the correct answer.
Solve the inequality: (5x)/2 - 3 ≤ 7
x ≤ 4
x < 4
x ≥ 4
x > 4
Adding 3 to both sides gives (5x)/2 ≤ 10; multiplying by 2 and then dividing by 5 isolates x and results in x ≤ 4. Hence, x ≤ 4 is correct.
Solve the inequality: 3x + 5 > 2x + 9
x > 4
x ≥ 4
x < 4
x ≤ 4
Subtracting 2x from both sides gives x + 5 > 9, and subtracting 5 leads to x > 4. Thus, x > 4 is the correct answer.
Solve the inequality: 6 - 2x < 0
x > 3
x < 3
x ≥ 3
x ≤ 3
Subtracting 6 leads to -2x < -6; dividing by -2 (and flipping the inequality sign) yields x > 3. Therefore, x > 3 is correct.
Solve the inequality: (2x - 1)/3 > 3
x > 5
x ≥ 5
x < 5
x ≤ 5
Multiplying both sides by 3 gives 2x - 1 > 9; adding 1 and dividing by 2 isolates x and results in x > 5. Hence, x > 5 is correct.
Solve the inequality: -3x + 7 < 1
x ≥ 2
x > 2
x ≤ 2
x < 2
Subtracting 7 gives -3x < -6; dividing by -3 (and flipping the inequality) yields x > 2. Therefore, x > 2 is correct.
Solve the inequality: 4 - 2(3x + 1) ≥ -6
x ≥ 4/3
x ≤ 4/3
x > 4/3
x < 4/3
Expanding gives 4 - 6x - 2 which simplifies to 2 - 6x ≥ -6; subtracting 2 and dividing by -6 (with reversal) results in x ≤ 4/3. Hence, x ≤ 4/3 is correct.
Solve the inequality: -5 + 2x < 3x + 1
x > -6
x < -6
x ≥ -6
x ≤ -6
By subtracting 2x from both sides, we obtain -5 < x + 1; subtracting 1 gives x > -6. Thus, x > -6 is correct.
Solve the inequality: 8 - (x + 2) ≤ 3
x ≥ 3
x ≤ 3
x > 3
x < 3
Simplifying the inequality gives 6 - x ≤ 3; subtracting 6 results in -x ≤ -3, and multiplying by -1 (with reversal) produces x ≥ 3. Therefore, x ≥ 3 is correct.
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Study Outcomes

  1. Solve two-step inequalities by applying inverse operations.
  2. Analyze the impact of arithmetic operations on inequality direction.
  3. Apply logical reasoning to isolate the variable in multi-step problems.
  4. Express solutions in both inequality and interval notation.
  5. Verify solutions through substitution and estimation techniques.

Two Step Inequalities Worksheet PDF Cheat Sheet

  1. Understand two-step inequalities - Two-step inequalities involve two inverse operations - like subtraction followed by division - to isolate the variable. Think of it as unwrapping a present in reverse order: you undo one layer, then the next. Once you get the hang of it, you'll breeze through these problems! Mathcation: Two-step inequalities
  2. Reverse the inequality sign with negatives - Whenever you multiply or divide both sides by a negative number, the inequality sign flips direction. It's like turning the sign upside down - don't let that sneaky minus catch you off guard! Always double‑check this step to keep your solution valid. Socratic: Solving two-step inequalities
  3. Follow the inverse order of operations - Solve by undoing addition or subtraction first, then tackle multiplication or division. Imagine backtracking your steps: what you did last, you undo first! This method keeps your work neat and errors at bay. ShowMeTheMath: Two-step practice
  4. Know your inequality symbols - Get comfy with >, <, ≥, and ≤ so you know exactly which values are included or excluded. Visual cues like open versus closed circles on graphs help you remember endpoints. Master these symbols, and the rest of the problem becomes a breeze! Symbolab: Inequality symbols guide
  5. Check solutions by substitution - Plug your answer back into the original inequality to confirm it works. This quick "plug‑and‑play" trick catches mistakes before they sneak into your final answer. It's like having a built‑in safety net for your work! Tutoring Hour: Two-step checks
  6. Translate word problems into inequalities - Carefully read the scenario and turn phrases like "at least" or "no more than" into the correct inequality symbols. Treat it as a secret code-breaking mission where every word matters. Once you decode it, the solving part is straightforward! Tutoring Hour: Word problems
  7. Graph solutions on a number line - Plotting your solution gives a visual map of possible values and whether endpoints are included. Open circles mean "not included," closed circles mean "welcome aboard." This sketch helps you see the big picture at a glance! Online Math Learning: Graphing inequalities
  8. Avoid common sign-flip mistakes - Create a quick mental checklist: did you flip the sign when you should've? Did you perform operations in the right order? A tiny slip can change your answer completely, so double‑check each step. Mathcation: Avoid sign errors
  9. Use interval notation - Express solution sets compactly with brackets [ ] and parentheses ( ). Brackets include endpoints, parentheses exclude them - it's like math shorthand! This notation makes your answers look crisp and professional. Symbolab: Interval notation
  10. Practice with worksheets and quizzes - Regular drills build speed and confidence, turning tricky problems into routine wins. Mix timed quizzes with varied question types to cover all your bases. The more you practice, the more these steps become second nature! Mathcation: Practice worksheets
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