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Quizzes > High School Quizzes > Mathematics

6th Grade Inequalities Practice Quiz

Sharpen your math skills with integers practice

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Paper art promoting Integer and Inequality Quest trivia for middle school math students.

What is the result of adding -3 and 5?
2
-8
8
1
Adding -3 and 5 gives 2 because -3 + 5 equals 2. This demonstrates how adding a negative number is equivalent to subtracting its absolute value.
Which inequality represents 'x is at least 7'?
x ≥ 7
x > 7
x ≤ 7
x < 7
The phrase 'at least 7' means that x can be 7 or any number greater. Thus, x must be greater than or equal to 7.
Which integer is the smallest: -5, 0, 3, or -2?
-5
0
3
-2
On the number line, -5 is to the left of -2, 0, and 3, making it the smallest value among the options.
What is the value of -8 - (-3)?
-5
-11
5
1
Subtracting a negative number is the same as adding its positive equivalent, so -8 - (-3) is equal to -8 + 3, which gives -5.
Which statement is true about integers on a number line?
Each integer has a unique location on the number line.
Every integer is positive.
Integers include fractions.
Zero is not an integer.
Every integer, whether negative, zero, or positive, occupies a distinct spot on the number line. This understanding helps in visualizing integer relationships.
Solve the inequality: x + 2 < 7.
x < 5
x < 7
x < 9
x ≤ 5
Subtracting 2 from both sides of x + 2 < 7 yields x < 5. The inequality remains strict after subtracting the same number from both sides.
Solve for x: -2x > 6.
x < -3
x > -3
x < 3
x > 3
Dividing both sides by -2 reverses the inequality sign, resulting in x < -3. This is a common step when solving inequalities with negative coefficients.
Which inequality represents all x such that 3 ≤ x < 8?
3 ≤ x < 8
3 < x ≤ 8
3 < x < 8
3 ≤ x ≤ 8
The notation 3 ≤ x < 8 indicates that x can be equal to 3 but must be less than 8. This is the precise way of expressing the given range.
Determine the value of | -15 |.
15
-15
0
30
The absolute value of a number represents its distance from zero, regardless of sign. Therefore, | -15 | is 15.
If -4 > x, which of these is a possible value for x?
-5
-3
0
4
Since x must be less than -4, -5 qualifies as a correct value. The other options do not satisfy the inequality.
Solve the inequality: 5 - x ≤ 8.
x ≥ -3
x ≤ -3
x > -3
x < -3
Subtract 5 from both sides to get -x ≤ 3. Multiplying both sides by -1 (and reversing the inequality) results in x ≥ -3.
What is the sum of the integers: -7 + 4 + 2?
-1
-5
3
-2
Adding -7 and 4 gives -3, and when you add 2 the result is -1. This question tests the basic operation with negative integers.
Solve the compound inequality: -1 < 2x + 3 < 7.
-2 < x < 2
-2 ≤ x ≤ 2
-1 < x < 3
x < 2
Subtract 3 from all parts to obtain -4 < 2x < 4, and then divide by 2 to get -2 < x < 2. This shows the step-by-step process in solving compound inequalities.
Which inequality describes 'x is no more than 10'?
x ≤ 10
x < 10
x ≥ 10
x > 10
The phrase 'no more than' means x can be equal to 10 or less. Hence, x ≤ 10 is the appropriate inequality.
Solve for x: -3x + 5 > 2.
x < 1
x > 1
x ≤ 1
x ≥ 1
Subtract 5 from both sides to get -3x > -3 and then divide by -3 while reversing the inequality sign, which results in x < 1.
Solve for x: 2(x - 4) < 3x + 1.
x > -9
x < -9
x ≥ -9
x ≤ -9
First, distribute to obtain 2x - 8 < 3x + 1. Subtracting 2x from both sides gives -8 < x + 1 and then subtracting 1 yields x > -9.
Solve for x: -3(x + 2) ≥ 2x - 6.
x ≤ 0
x ≥ 0
x < 0
x > 0
Distribute to get -3x - 6 ≥ 2x - 6. Adding 3x to both sides results in -6 ≥ 5x - 6; then adding 6 to both sides gives 0 ≥ 5x, which simplifies to x ≤ 0.
Find the solution set for the inequality |x - 2| > 5.
x > 7 or x < -3
-3 ≤ x ≤ 7
x ≥ 7 or x ≤ -3
-7 < x < 3
The inequality |x - 2| > 5 splits into two cases: x - 2 > 5 (which gives x > 7) or x - 2 < -5 (which gives x < -3). Both conditions together describe the solution set.
Which expression is equivalent to solving 3 - 2x ≤ 7 for x?
x ≥ -2
x ≤ -2
x > -2
x < -2
Subtracting 3 from both sides yields -2x ≤ 4. Dividing by -2 while flipping the inequality sign leads to x ≥ -2, which is the correct equivalent expression.
Determine the solution set for the inequality: 4 - 2(3 - x) > 10.
x > 6
x < 6
x ≥ 6
x ≤ 6
First, expand the expression to get 4 - 6 + 2x > 10, which simplifies to 2x - 2 > 10. Adding 2 and then dividing by 2 produces the result x > 6.
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Study Outcomes

  1. Analyze integer operations and their properties.
  2. Apply inequality rules to solve mathematical problems.
  3. Interpret and represent inequality solutions on a number line.
  4. Evaluate problem scenarios to determine relationships between integers.
  5. Create strategies for solving integer and inequality challenges.

6th Grade Inequalities & Integers Cheat Sheet

  1. Recognize inequality symbols - Spotting <, >, ≤, and ≥ is your first step to acing any inequality problem. Once you know which way those arrows point, you'll breeze through interpreting expressions. Inequalities Practice Questions with Solution | GeeksforGeeks
  2. Master inequality properties - Adding or subtracting the same value on both sides keeps the inequality direction, but multiplying or dividing by a negative flips it. Remembering this rule is like having a superpower when you solve more complex puzzles. Study Guide - Linear Inequalities in One Variable
  3. Crack one-step inequalities - Isolate the variable in a snap: for x − 5 > 3, just add 5 to get x > 8. Practicing these quick moves builds confidence before you move on. Solving Inequalities by Addition and Subtraction: Study Guide
  4. Tackle two-step inequalities - Combine inverse operations: solve 2x + 3 ≤ 7 by subtracting 3, then divide by 2 to get x ≤ 2. Breaking it into clear steps makes even multi-step challenges fun. Linear Inequalities Practice Questions | GeeksforGeeks
  5. Decode compound inequalities - "And" or "or" can string two inequalities together: - 2 < x + 1 ≤ 5 translates to - 3 < x ≤ 4. Visualizing the solution range helps you see the whole picture. Inequalities Practice Questions with Solution | GeeksforGeeks
  6. Graph on a number line - Use open circles for < or > and closed circles for ≤ or ≥, then shade in the solution direction. A clear sketch turns abstract answers into colorful real-life lines. Inequalities: Study Guide | SparkNotes
  7. Conquer absolute value inequalities - Split |x - 3| > 4 into x - 3 > 4 or x - 3 < - 4, then solve each part. This two-for-one trick helps you tame even the trickiest expressions. Inequalities Practice Questions with Solution | GeeksforGeeks
  8. Solve with variables on both sides - For 3x - 2 > x + 4, get all x terms one side (3x - x), then collect constants (4 + 2) to find x > 3. Balancing like a pro means fewer mistakes down the road. Linear Inequalities Practice Questions | GeeksforGeeks
  9. Express solutions in interval notation - Write x > 2 as (2, ∞) or x ≤ 5 as ( - ∞, 5]. This shorthand keeps your answers neat and universally understood. Study Guide - Linear Inequalities in One Variable
  10. Apply inequalities to real life - From budgeting limits to ingredient ratios, inequalities help model countless scenarios. Practicing with fun examples makes math feel like a superpower you can use every day. Inequalities: Study Guide | SparkNotes
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