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Quizzes > High School Quizzes > Mathematics

2b Equivalent Expression Practice Quiz

Practice problems to master equivalent expressions

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art illustration promoting the 15 5 2b Challenge, a rigorous math quiz for middle school students.

What is the simplified form of the expression 2x + 3x?
6x
5
x^2
5x
By combining like terms, 2x + 3x equals (2+3)x, which gives 5x. The other options do not correctly combine the coefficients.
What is the result of applying the distributive property to 3(x + 4)?
x + 7
3x + 12
4x + 3
3x + 4
Multiplying 3 by each term inside the parentheses gives 3x + 12. The other options come from either incomplete distribution or misapplication of the property.
Simplify the expression x + x + x.
x
3x
2x
x^2
Adding the three identical terms x results in 3x. The other options reflect common mistakes such as incorrect multiplication or combining of terms.
Which expression is equivalent to 5 - 2x + 3?
8 + 2x
8 - 2x
2x - 8
5 - 2x
Combining the constant terms 5 and 3 gives 8, so the expression becomes 8 - 2x. The remaining options do not combine constants properly.
What is the simplified form of the expression 6a - 4a?
10a
2a
6a
a
Subtracting like terms (6a - 4a) results in 2a. The other options represent errors in the subtraction process.
Simplify and combine like terms: 2x + 3 - x + 5.
3x + 8
x + 15
2x + 15
x + 8
Subtracting x from 2x gives x, and adding the constants 3 and 5 results in 8, so the simplified expression is x + 8. The other options combine terms incorrectly.
Distribute and simplify: 4(2y - 3) + 5y.
8y - 12
13y - 12
9y - 12
13y + 12
Distributing 4 gives 8y - 12, and adding 5y results in 13y - 12. The other options likely emerge from misapplication of distribution or addition errors.
Factor the expression: 6x + 9.
3(2x + 3)
6(x + 3)
(2x + 3)
3(2x + 9)
The greatest common factor of 6x and 9 is 3, so factoring yields 3(2x + 3). The other choices either factor incorrectly or omit the common factor.
Simplify: 2(3x - 4) - (x - 6).
5x - 10
6x - 2
5x + 2
5x - 2
Expanding the terms gives 6x - 8 from the first part and -x + 6 from the second, which combine to 5x - 2. The incorrect options reflect errors in handling the negative sign or in combining like terms.
Which expression is equivalent to 4x + 12 when factored?
3(x + 4)
4(x - 3)
2(x + 6)
4(x + 3)
Factoring out the common factor 4 from 4x + 12 yields 4(x + 3). The other options either use an incorrect factor or have the wrong sign.
Simplify the expression: 3a + 2b - a + 4b.
4a + 2b
3a + 6b
2a + 6b
2a + 4b
Combine like terms to get (3a - a) which equals 2a, and (2b + 4b) which equals 6b, resulting in 2a + 6b. The other answers show mistakes in combining the coefficients.
Apply the distributive property: -2(3x - 4).
-6x - 8
6x - 8
6x + 8
-6x + 8
Multiplying -2 by 3x gives -6x and by -4 gives +8, which yields -6x + 8. The other options arise from mismanaging the negative signs during multiplication.
What is the simplified form of the expression: 5(x + 2) - 3(x - 4)?
2x + 22
2x - 2
8x + 6
2x + 6
Expanding gives 5x + 10 and -3x + 12, and combining like terms results in 2x + 22. The other options indicate errors that could occur during distribution or addition.
Which expression is equivalent to 0.5(4x + 10)?
4x + 5
2x + 10
2x + 5
0.5x + 10
Distributing 0.5 gives 2x and 5, so the expression simplifies to 2x + 5. The remaining options do not correctly apply the multiplication factor to both terms.
Factor the expression: 8y + 20.
8(y + 5)
2(4y + 5)
4(2y + 5)
2(2y + 10)
The greatest common factor of 8y and 20 is 4, leading to the factored form 4(2y + 5). The other options factor incorrectly and do not simplify to the original expression.
Determine which of the following expressions is equivalent to 3(x - 2) + 2(2x + 1).
5x - 4
7x + 4
5x + 4
7x - 4
Expanding the expressions gives 3x - 6 and 4x + 2, which combine to 7x - 4. The other alternatives are the result of errors in expansion or combining like terms.
Simplify the complex expression: 2[3(x + 2) - 4] - 5(x - 1).
x + 9
x + 7
x - 1
5x + 9
First, simplify inside the brackets to get 3x + 6 - 4 = 3x + 2. Multiplying by 2 gives 6x + 4, and subtracting 5x - 5 results in x + 9. The distractors reflect errors in distribution or combining like terms.
If 4(2x - 3) is equivalent to 8x + k, what is the value of k?
3
-12
-3
12
Expanding 4(2x - 3) yields 8x - 12, so k must be -12 to match the form 8x + k. The other options do not satisfy the expanded expression.
Which expression is equivalent to 2x - (3x - 4)?
-x + 4
-5x + 4
x - 4
5x - 4
Distributing the negative sign inside the parentheses gives 2x - 3x + 4, which simplifies to -x + 4. The other options are typical errors when handling subtraction of expressions.
Simplify the expression: 3(2y + 4) - 2(y - 3) + y.
7y + 6
7y + 18
5y + 6
5y + 18
Expanding each term gives 6y + 12, -2y + 6, and an additional y. Combining like terms leads to 5y + 18. The other options reflect miscalculation during distribution or combining terms.
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Study Outcomes

  1. Apply arithmetic operations and the order of operations to calculate expressions accurately.
  2. Simplify algebraic expressions by combining like terms and using distributive properties.
  3. Analyze equivalent expressions to recognize underlying mathematical relationships.
  4. Translate verbal problem statements into accurate mathematical expressions.
  5. Develop effective problem-solving strategies to tackle multi-step arithmetic and algebra challenges.

15 5 2b Equivalent Expression Cheat Sheet

  1. Master the Distributive Property - Think of the distributive property as your go‑to move for spreading multiplication across addition, turning a(b + c) into ab + ac with ease. It's the ultimate simplifier when you need to break down and conquer more complex expressions. Practice this trick, and watch those tough problems shrink before your eyes! Equivalent Expressions Worksheet
  2. Combine Like Terms - Group together terms with the same variables and exponents to make your expressions lean and mean - 3x + 5x instantly becomes 8x! This streamlines calculations and keeps your work neat and tidy. Spend a few minutes each day matching like terms, and you'll master this skill in no time. Seventh Grade Expression Worksheet
  3. Understand the Commutative Property - Remember, order doesn't matter when you're adding or multiplying: a + b = b + a. This flexibility helps you shuffle pieces of an expression into the perfect arrangement for quick simplification. Keep this property in your toolkit to spot shortcuts and speed through problems! Commutative Property Practice
  4. Apply the Associative Property - Whether you're adding or multiplying, how you group numbers won't change the result: (a + b) + c = a + (b + c). Use this to rearrange and simplify multi‑step expressions without breaking a sweat. It's like rearranging furniture: the pieces are the same, but the room feels totally fresh and organized! Associative Property Guide
  5. Practice Factoring Expressions - Flip the distributive property on its head by turning sums into products, like rewriting ab + ac as a(b + c). Factoring is a huge advantage when solving equations or spotting hidden patterns. Make it a habit, and you'll start seeing factored forms everywhere - in no time, you'll be factoring like a pro! Factoring Worksheet
  6. Use Substitution to Verify Equivalence - Give both sides of an expression your favorite numbers, and see if they match - if they do, congratulations, you've just proved equivalence! This method is a fail‑safe way to check your work and build confidence. Grab some random values, plug them in, and enjoy the "aha!" moments when everything lines up. Substitution Practice
  7. Recognize Standard and Expanded Forms - Spot the difference between 5(x + 2) (factored form) and 5x + 10 (expanded form), and learn to switch back and forth like a shape‑shifting champ. Knowing both forms helps you adapt to any problem that comes your way. Flip between them smoothly, and you'll conquer homework faster than ever! Form Conversion Guide
  8. Simplify with Inverse Operations - Use additive inverses (adding the opposite) and multiplicative inverses (multiplying by the reciprocal) to cancel terms and simplify expressions in a flash. It's like having a "math eraser" that wipes away unwanted pieces. Master these inverses to solve equations in just a couple of steps! Inverse Operations Practice
  9. Practice with Interactive Worksheets - Level up your study sessions with digital worksheets that give instant feedback and fun challenges. Interactive problems help solidify your understanding and keep you engaged. Carve out a few minutes daily to power through these drills and watch your skills skyrocket! Interactive Practice
  10. Utilize Matching Activities - Boost your pattern‑recognition skills by matching equivalent expressions in speed‑round style. These quick‑fire exercises train your brain to spot relationships in record time. Grab a timer, shuffle those cards, and turn practicing into a fast‑paced game! Matching Activity
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