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

Equivalent Equations Practice Quiz

Improve your skills with easy equation solving worksheets

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art promoting Equations Made Easy, a math trivia quiz for middle and high school students.

Solve for x in the equation 2x + 3 = 11. What is the value of x?
x = 14
x = 7
x = 8
x = 4
Subtracting 3 from both sides gives 2x = 8, and dividing by 2 isolates x, resulting in x = 4. This straightforward operation demonstrates the basic principle of inverse operations.
What property of equality is demonstrated when the same number is added to both sides of an equation?
Division property of equality
Subtraction property of equality
Addition property of equality
Multiplication property of equality
Adding the same number to both sides of an equation maintains its balance, which is known as the addition property of equality. This property ensures that the equality holds after the operation is performed.
If you have the equation x - 4 = 5 and you add 4 to both sides, what equivalent equation do you get?
x = 5
x - 9 = 0
4x = 5
x = 9
Adding 4 to both sides cancels out the -4 on the left, resulting in x = 5 + 4, which simplifies to x = 9. This demonstrates the proper use of the addition property to isolate the variable.
Which step correctly solves the equation 3 + x = 7?
Subtract x from both sides to get 3 = 7 - x
Divide 7 by 3
Subtract 3 from both sides to get x = 4
Add 7 to both sides
Subtracting 3 from both sides removes the constant from the left side, leaving x isolated as x = 4. This simple subtraction is the proper initial step to solve for x.
If 2x = 10, what is the value of x?
x = -5
x = 5
x = 10
x = 20
Dividing both sides by 2 isolates x, yielding x = 5. This problem exemplifies the division property of equality, which is fundamental in solving linear equations.
Solve for x: 3(x - 2) = 9. What is the value of x?
x = -5
x = 7
x = 5
x = 3
First, distribute 3 to obtain 3x - 6 = 9. Then add 6 to both sides and divide by 3, which results in x = 5. This problem reinforces the concept of distribution followed by isolation of the variable.
Given the equation 4x + 2 = 18, what is the correct sequence of steps to solve for x?
Divide both sides by 4, then subtract 2
Subtract 2 from both sides, then divide by 4
Add 2 to both sides, then divide by 4
Multiply both sides by 4, then subtract 2
Subtracting 2 first removes the constant from the left side, leaving 4x = 16. Dividing by 4 then isolates x, showing the proper order of operations in solving the equation.
Determine the value of y in the equation 2(y + 3) = 16.
y = 8
y = 5
y = 2
y = 6
Expanding the left side gives 2y + 6 = 16. Subtracting 6 and then dividing by 2 results in y = 5. This problem illustrates the use of distribution and subsequent isolation of the variable.
Find the value of x in the equation x + 4 - 2x = 3.
x = -1
x = 0
x = 1
x = 7
Combining like terms results in -x + 4 = 3. Subtracting 4 from both sides and then multiplying by -1 gives x = 1. This reinforces the skill of combining like terms in an equation.
Solve for x: 2x - 3 = 3x + 1.
x = -4
x = 2
x = 4
x = -2
Subtracting 2x from both sides gives -3 = x + 1. Further subtracting 1 isolates x, resulting in x = -4. This question tests the ability to shift terms across the equation.
What is the nature of the equation 3x + 2 = 2 + 3x?
It has no solution
Its truth depends on the value of x
It has a unique solution, x = 0
It is an identity; it is true for all real numbers
Subtracting 3x from both sides eliminates the variable, leaving 2 = 2, which is always true. This indicates that the equation is an identity and holds for all values of x.
Solve for x in the equation -2(x - 4) = 6.
x = 2
x = -1
x = -2
x = 1
Distribute -2 to obtain -2x + 8 = 6. Subtracting 8 from both sides gives -2x = -2, and dividing by -2 results in x = 1. This reinforces the method of distribution followed by isolation.
Which of the following describes the correct method to solve the equation 7 + 2x = 19?
Subtract 2x from both sides
Multiply both sides by 2 and then subtract 7
Divide 19 by 2 and then subtract 7
Subtract 7 from both sides and then divide by 2 to isolate x (x = 6)
Subtracting 7 from both sides simplifies the equation to 2x = 12, and dividing by 2 yields x = 6. This step-by-step process exemplifies proper equation solving.
Solve for x: 2(x + 3) + 4 = 18.
x = 4
x = 5
x = 7
x = 6
Expanding gives 2x + 6 + 4 = 18, which simplifies to 2x + 10 = 18. Subtracting 10 and then dividing by 2 isolates x, resulting in x = 4.
Solve for x: 2(x - 1) = x + 2.
x = 3
x = 4
x = 0
x = 2
Distribute 2 to get 2x - 2 = x + 2. Subtracting x from both sides results in x - 2 = 2, and adding 2 isolates x, giving x = 4. This question tests combining like terms and using inverse operations.
Solve for x: (x/3) + 2 = (x/6) + 5.
x = 15
x = 12
x = 18
x = 20
Multiplying the entire equation by 6 eliminates the fractions, yielding 2x + 12 = x + 30. Subtracting x and then 12 isolates x, resulting in x = 18.
Determine the solution for x in the equation: 3(2x - 4) - (x + 2) = 2x + 10.
x = 12
x = 10
x = 8
x = 6
Expanding the expression gives 6x - 12 - x - 2, which simplifies to 5x - 14. Setting this equal to 2x + 10 and solving for x results in x = 8.
Solve for x in the equation: (x - 2)/4 = (x + 6)/8.
x = 12
x = 5
x = 10
x = 8
Multiplying both sides by 8 removes the denominators, leading to 2(x - 2) = x + 6. Solving this linear equation gives x = 10.
After simplifying the equation 2(x + 3) - 4 = x + 8, which equivalent equation is correct before solving for x?
x - 2 = 8
2x - 2 = 8
2x + 2 = 8
x + 2 = 8
Distributing and combining like terms yields 2x + 6 - 4 = 2x + 2 on the left side. Equating this to x + 8 and subtracting x provides the equivalent equation x + 2 = 8.
Solve for x in the equation: 5 - 2(3 - x) = 3x + 1.
x = -2
x = 1
x = 2
x = -1
Distributing -2 over (3 - x) gives -6 + 2x, and adding 5 results in 2x - 1 on the left side. Setting this equal to 3x + 1 and solving for x leads to x = -2.
0
{"name":"Solve for x in the equation 2x + 3 = 11. What is the value of x?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"Solve for x in the equation 2x + 3 = 11. What is the value of x?, What property of equality is demonstrated when the same number is added to both sides of an equation?, If you have the equation x - 4 = 5 and you add 4 to both sides, what equivalent equation do you get?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand the structure of equivalent equations.
  2. Simplify algebraic expressions using inverse operations.
  3. Apply techniques to isolate variables in equations.
  4. Analyze solutions to verify their accuracy.
  5. Enhance problem-solving skills for exam preparation.

Equivalent Equations Cheat Sheet

  1. Understanding Equivalent Equations - Think of equivalent equations as different road maps leading to the same treasure. They share the same solution even if they wear different outfits. Mastering this concept speeds up your solving game. ThoughtCo: Equivalent Equations Explained
  2. Applying the Addition and Subtraction Properties - Balance is everything! Adding or subtracting the same number on both sides keeps your equation fair and unchanged. Get comfortable shifting terms and you'll breeze through steps like a pro. ThoughtCo: Addition & Subtraction Tips
  3. Utilizing the Multiplication and Division Properties - Your secret weapon for isolating variables: multiply or divide both sides by the same nonzero number. This trick transforms complicated equations into simple "x =" form. Just double‑check you never divide by zero or you'll summon the math police! ThoughtCo: Multiply & Divide Strategies
  4. Combining Like Terms - Squish your equation down by gathering like terms on each side. Turning 3x + 2x into 5x is like turning clutter into clarity. Fewer terms mean fewer hassles when solving. Mathcation: Equivalent Expressions
  5. Using the Distributive Property - Break out the parentheses and distribute like a pro! Converting 2(x + 3) into 2x + 6 opens the door to simpler steps. This move clears complexity with surgical precision. Mathcation: Distributive Property Guide
  6. Recognizing Infinite and No Solution Cases - Sometimes equations are overachievers with infinite solutions or rebels with none. For example, 2x + 3 = 2x + 3 accepts any x, while x + 2 = x + 5 is a flat‑out contradiction. Spot these cases early to save time and sanity. Online Math Learning: Special Cases
  7. Practicing with Real‑World Problems - When you apply equations to pizza slices or pocket money, math clicks into place. Modeling discounts or totals brings theory to life and makes practice feel relevant. Real‑world applications cement your skills and earn you bragging rights. Pedagogue: Real‑World Activities
  8. Exploring Different Forms of Linear Equations - Slope‑intercept? Point‑slope? These are just different costumes for the same algebraic star. Converting y = 2x + 3 into y - 3 = 2(x - 0) shows how forms stay equivalent yet flexible. SparkNotes: Writing Equations
  9. Engaging in Interactive Activities - Balance scales, card games, or equation puzzles make abstract algebra feel like a carnival. Hands‑on tasks help your brain "get" balance and equivalence. Plus, they're way more fun than staring at a textbook! Pedagogue: Interactive Exercises
  10. Utilizing Online Resources and Worksheets - Dive into quizzes, interactive worksheets, and tutorial videos to level up your skills. Extra practice with fresh problem sets locks in your understanding and builds confidence. Let digital tools be your trusty study sidekicks! Mathcation: Practice Worksheets
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker