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Quizzes > High School Quizzes > Mathematics

Equations and Inequalities Quick Check Practice Quiz

Master equations, tackle worksheets, and ace practice questions

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art representing a trivia quiz on equations and inequalities for high school students.

What is the solution for x in the equation x + 5 = 12?
x = 7
x = 5
x = 12
x = 17
Subtracting 5 from both sides of the equation gives x = 7. This method confirms the result because adding 5 back to 7 returns 12.
What is the solution to the equation 3x = 9?
x = 3
x = 6
x = 9
x = 12
Dividing both sides of the equation by 3 yields x = 3. This straightforward division verifies the correct solution.
Solve for x: 2(x - 1) = 8.
x = 5
x = 4
x = 6
x = 8
First, distribute to get 2x - 2 = 8. Adding 2 to both sides and then dividing by 2 leads to x = 5.
Solve the inequality: x - 3 > 2.
x > 5
x < 5
x ≥ 5
x ≤ 5
By adding 3 to both sides of the inequality, you obtain x > 5. This simple adjustment confirms that the solution set consists of values greater than 5.
Find x if 4x = 20.
x = 5
x = 4
x = 20
x = 6
Dividing both sides of the equation by 4 results in x = 20/4, which simplifies to x = 5. The calculation directly confirms the correct answer.
Solve for x: 2x + 3 = 3x - 2.
x = 5
x = -5
x = 2
x = -2
Subtracting 2x from both sides gives 3 = x - 2, and then adding 2 to each side results in x = 5. This standard method for equations with variables on both sides leads to the correct answer.
Solve the inequality: 3x - 4 ≤ 2x + 1.
x ≤ 5
x < 5
x ≥ 5
x > 5
By subtracting 2x from both sides, the inequality becomes x - 4 ≤ 1. Adding 4 to both sides gives x ≤ 5, which is the correct solution.
Find the solution of the equation: 5(x - 2) = 3x + 4.
x = 7
x = 6
x = 8
x = 14
Expanding the left side gives 5x - 10, and setting the equation 5x - 10 = 3x + 4 leads to 2x = 14 after rearrangement. Dividing by 2 yields x = 7, confirming the correct answer.
What is the solution for x in the equation: x/2 + 3 = 7?
x = 8
x = 4
x = 10
x = 14
Subtracting 3 from both sides transforms the equation into x/2 = 4. Multiplying both sides by 2 then gives x = 8, which is the correct solution.
Solve for x: 4(x + 2) - 3(2x - 1) = 5.
x = 3
x = 2
x = -3
x = 6
Distributing the terms gives 4x + 8 - 6x + 3, which simplifies to -2x + 11 = 5. Solving for x yields x = 3 after moving terms and dividing by -2.
Find the value of x: 2(x - 3) + 3 = x + 4.
x = 7
x = 6
x = 5
x = 4
Expanding the left side results in 2x - 6 + 3, which simplifies to 2x - 3 = x + 4. Subtracting x and then adding 3 gives x = 7, confirming the answer.
Which of the following is a solution to the inequality 2x + 1 > 7?
x = 4
x = 3
x = 2
x = 1
Subtracting 1 from both sides produces 2x > 6, and dividing by 2 results in x > 3. Therefore, the value x = 4 is the only option that satisfies this condition.
Solve for y: 3y - 5 = 2y + 1.
y = 6
y = 5
y = 1
y = 7
Subtracting 2y from both sides gives y - 5 = 1, and adding 5 to both sides results in y = 6. This clear, step-by-step process confirms the answer.
Find the value of x that satisfies: 4x - 2(x + 3) = x - 8.
x = -2
x = 2
x = -6
x = 6
Expanding the expression gives 4x - 2x - 6 = x - 8, which simplifies to 2x - 6 = x - 8. Solving for x yields x = -2 after isolating the variable.
Solve the compound inequality: 2 < x + 1 ≤ 5.
1 < x ≤ 4
2 < x ≤ 5
1 ≤ x < 4
2 ≤ x < 5
Subtracting 1 from every part of the inequality results in 1 < x ≤ 4. This method correctly isolates x and maintains the integrity of the inequality.
Solve for x: (x/3) + (1/2) = (5/6).
x = 1
x = 2
x = 3
x = 6
Multiplying every term by 6, the least common denominator, transforms the equation into 2x + 3 = 5. Solving this simplified equation yields x = 1, which is the correct answer.
Solve the inequality: -2(x - 3) < 4.
x > 1
x < 1
x ≥ 1
x ≤ 1
Distributing -2 gives -2x + 6 < 4. After subtracting 6 and dividing by -2 (which reverses the inequality), the solution is x > 1.
Solve the equation: 3(x - 2) + 2(2x + 1) = 4(x + 1) + x.
x = 4
x = 3
x = 2
x = 6
Expanding both sides results in 3x - 6 + 4x + 2 = 7x - 4 on the left and 4x + 4 + x = 5x + 4 on the right. Simplifying leads to 7x - 4 = 5x + 4, and solving for x gives x = 4.
Determine the value of x: 2(x + 4) - (3x - 5) = x + 9.
x = 2
x = 4
x = -2
x = -4
Expanding the left side gives 2x + 8 - 3x + 5, which simplifies to -x + 13. Setting this equal to x + 9 and solving for x results in x = 2.
If 2(x - 3) = (x + 5) - 4, what is the value of x?
x = 7
x = 6
x = 5
x = 8
First, expand the left side to get 2x - 6. The right side simplifies to x + 1, leading to the equation 2x - 6 = x + 1. Solving this yields x = 7, which is the correct answer.
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Study Outcomes

  1. Analyze linear equations and inequalities using fundamental algebraic techniques.
  2. Simplify and solve equations by isolating variables and combining like terms.
  3. Apply problem-solving strategies to tackle a variety of algebra challenges.
  4. Interpret and validate solutions in the context of word problems and real-life scenarios.
  5. Evaluate the properties of equations and inequalities to determine the most efficient solving methods.

Equations & Inequalities Quick Check Cheat Sheet

  1. Master solving linear equations - Dive into isolating variables step by step, like subtracting 5 from both sides of 3x + 5 = 20, then dividing by 3 to reveal x = 5. With each practice problem you'll build confidence and speed, making those "aha!" moments a daily ritual. PERT Math Study Guide: Equations & Inequalities
  2. Flip the sign when negatives strike - Remember, multiplying or dividing an inequality by a negative flips its direction. Tackle problems like - 2x > 4 by flipping the "greater than" to "less than" when you divide, then watch the solution fall into place. PERT Math Study Guide: Equations & Inequalities
  3. Graph inequalities with style - Sketch number lines and shade the solution region to visualize expressions like x ≤ 4, where every point up to 4 shines. This visual strategy cements your understanding and turns abstract concepts into clear, colorful diagrams. Inequalities: Study Guide | SparkNotes
  4. Crack systems of equations - Use substitution or elimination to solve pairs like x + y = 3 and 2x - y = 0. These twin tactics help you uncover values effortlessly - just plug, solve, and celebrate when you get x = 1 and y = 2! Algebra: Systems of Equations and Inequalities
  5. Complete the square like a pro - Transform quadratics into (x - p)² = q format so solutions pop out naturally. This method not only solves equations but also deepens your grasp of how quadratics bend and shift. High School: Algebra » Reasoning with Equations & Inequalities » Solve equations and inequalities in one variable. » 4 » a | Common Core State Standards Initiative
  6. Apply the quadratic formula - Memorize x = [ - b ± √(b² - 4ac)]❄(2a) and decode any quadratic in one swoop. Don't forget the discriminant (b² - 4ac) - it's the secret key that tells you if roots are real, repeated, or complex! High School: Algebra » Reasoning with Equations & Inequalities » Solve equations and inequalities in one variable. » 4 » a | Common Core State Standards Initiative
  7. Tackle systems of inequalities - Graph multiple inequalities like y > 2x + 1 and y ≤ - x + 4, then identify the overlapping region where all conditions meet. It's like solving a puzzle - shade each area and watch the solution zone glow! Inequalities: Study Guide | SparkNotes
  8. Use the transitive property - If a > b and b > c, then a > c - simple, right? This foundational rule helps you chain comparisons together and keep inequalities on point. Inequalities: Study Guide | SparkNotes
  9. Translate word problems into equations - Turn real-world scenarios, like a rectangle whose length is 5 more than twice its width (and a perimeter of 36), into neat equations you can solve. Practice this skill to bridge everyday stories with algebraic power. Algebra: Systems of Equations and Inequalities
  10. Conquer absolute value challenges - Solve |x - 3| = 7 by splitting into x - 3 = 7 and x - 3 = - 7, covering both positive and negative cases. This approach ensures you catch every possible solution - no surprises here! Inequalities - High School Math
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