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Quizzes > High School Quizzes > Mathematics

Two-Step Equations Practice Quiz

Sharpen your skills with one- and multi-step problems

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting the 2-Step Equation Challenge, an engaging algebra quiz for middle schoolers.

Solve for x: x + 5 = 12.
5
17
7
12
Subtract 5 from both sides to isolate x, resulting in x = 7. This problem reinforces the basic two-step method of undoing addition to solve for the variable.
Solve for x: 2x - 4 = 8.
10
6
8
4
Add 4 to both sides to obtain 2x = 12, then divide by 2 to find x = 6. This exercise demonstrates the two-step approach: first undo subtraction, then division.
Solve for x: 4x + 3 = 19.
4
3
5
6
Subtract 3 from both sides to get 4x = 16, then divide by 4 to isolate x, yielding x = 4. This problem practices the sequential removal of constants and coefficients.
Solve for x: x/3 + 2 = 5.
15
6
3
9
Subtract 2 from both sides to get x/3 = 3, then multiply by 3 to find x = 9. This problem reinforces solving equations with fractional coefficients in a two-step process.
Solve for x: 3x - 2 = 10.
5
6
4
3
Add 2 to both sides to obtain 3x = 12, then divide by 3 to solve for x, resulting in x = 4. This straightforward problem highlights the inverse operations needed in a two-step equation.
Solve for x: 3x + 7 = 22.
8
7
4
5
Subtract 7 from both sides to obtain 3x = 15, then divide by 3 to solve for x, yielding x = 5. This reinforces the process of reversing addition followed by division.
Solve for x: 2x - 3 = 9.
5
6
9
7
Add 3 to both sides to yield 2x = 12, then divide by 2 to find x = 6. This problem highlights the sequential execution of addition and division in solving equations.
Solve for x: 4x - 5 = 3x + 1.
7
8
6
5
Subtract 3x from both sides to simplify the equation to x - 5 = 1, then add 5 to isolate x, resulting in x = 6. This question practices combining like terms before using inverse operations.
Solve for x: -2x + 4 = 10.
-3
6
-6
3
Subtract 4 from both sides to get -2x = 6, then divide by -2 to find x = -3. This introduces handling negative coefficients during the two-step solving process.
Solve for x: 5 - 3x = 2.
-1
3
1
2
Subtract 5 from both sides to obtain -3x = -3, then divide by -3 to isolate x, yielding x = 1. This exercise emphasizes the importance of managing negative terms in an equation.
Solve for x: 6x + 8 = 2x + 24.
3
8
4
6
Subtract 2x from both sides to get 4x + 8 = 24, then subtract 8 and divide by 4 yielding x = 4. This question reinforces the balancing of terms across the equation.
Solve for x: (3/2)x + 2 = 11/2.
7/3
7/2
5/3
2/3
Subtract 2 (written as 4/2) from 11/2 to get (3/2)x = 7/2, then multiply by the reciprocal of 3/2 to solve for x, resulting in x = 7/3. This problem demonstrates handling fractional coefficients in a two-step equation.
Solve for x: 2x - 7 = x + 2.
2
9
7
5
Subtract x from both sides to get x - 7 = 2, then add 7 to isolate x, yielding x = 9. This task reinforces combining like terms and executing inverse operations in sequence.
Solve for x: 5(x - 2) = 3x + 10.
12
10
8
5
Distribute 5 to obtain 5x - 10 = 3x + 10, then subtract 3x and add 10 to both sides; finally, divide by 2 to get x = 10. This problem integrates distribution with subsequent inverse operations.
Solve for x: 6 - 2(x + 1) = 4.
-2
0
2
4
First, distribute -2 over (x + 1) to get 6 - 2x - 2 = 4, which simplifies to 4 - 2x = 4. Then, subtract 4 from both sides and divide by -2, yielding x = 0.
Solve for x: 3(2x - 4) = 4x + 6.
6
8
12
9
Distribute 3 on the left-hand side to obtain 6x - 12 = 4x + 6. Then, subtract 4x from both sides and divide by 2 to find x = 9. This problem tests both distribution and combining like terms.
Solve for x: -3(x - 4) = 2x + 1.
11/5
5/11
11/3
-11/5
Expand the left-hand side to get -3x + 12 = 2x + 1, then add 3x to both sides and subtract 1 to get 11 = 5x. Dividing by 5 results in x = 11/5. This emphasizes careful handling of negative signs and distribution.
Solve for x: (x - 3)/2 + (x + 2)/3 = 5.
5
8
7
6
Multiply the entire equation by 6 to eliminate fractions, resulting in 3(x - 3) + 2(x + 2) = 30. Simplify to 5x - 5 = 30 and solve by adding 5 and dividing by 5, yielding x = 7.
Solve for x: (2/3)(x + 6) - 4 = x - 2.
8
3
4
6
Begin by expanding the left-hand side to get (2/3)x + 4 - 4 = x - 2, which simplifies to (2/3)x = x - 2. After clearing the fraction and rearranging, the solution is found to be x = 6. This exemplifies working with fractional coefficients and variable isolation.
Solve for x: 4(x + 2) - 3(2x - 1) = 5.
2
3
5
4
Distribute the numbers across the parentheses to obtain 4x + 8 - 6x + 3 = 5. Combine like terms to get -2x + 11 = 5, then subtract 11 and divide by -2 to solve for x, yielding x = 3. This problem integrates distribution with subsequent algebraic manipulation.
0
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Study Outcomes

  1. Understand how to isolate variables in two-step equations.
  2. Apply inverse operations to simplify and solve equations.
  3. Analyze problems to identify the steps necessary for solving two-step equations.
  4. Evaluate solutions to confirm the accuracy of the equation balancing.
  5. Develop confidence in applying algebraic techniques for solving equations.

1 & 2 Step Equations Cheat Sheet

  1. Master the Two-Step Magic - Every two-step equation needs two inverse moves to free the variable. Start by undoing addition or subtraction, then tackle multiplication or division. It's like unlocking a secret code in your algebra quest! Try GeeksforGeeks practice questions
  2. Know Your Order of Operations - In reverse-solving, always undo addition or subtraction first, then move on to multiplication or division. This keeps your steps neat and error-free, like following a treasure map. Consistency is the key to victory! Review with Online Math Learning
  3. Conquer Fractions - To zap away fractions, multiply both sides by the denominator. For example, if you see x/3 - 5 = 1, add 5, then multiply by 3 to reveal x. Think of it as multiplying your way to clarity! Fraction practice on GeeksforGeeks
  4. Tame Decimals - Decimals? No problem! Multiply the whole equation by a power of 10 to turn decimals into friendly whole numbers. It's a simple trick that makes calculations feel as smooth as skating on ice. Decimal tips at Online Math Learning
  5. Always Check Your Answer - After solving, plug your x (or y) back into the original equation to confirm it really works. Think of this as double-checking your game score to ensure you didn't miss any points. Confidence comes from verification! Check examples here
  6. Watch Out for Negatives - Multiplying or dividing by a negative number flips the sign, especially in inequalities. Missing this flip is like forgetting to open a hidden door - you'll end up stuck! Always pause and flip when needed. Practice negative flips at Mathcation
  7. Mix Up Your Practice - The more problem types you tackle, the more confident you become. Dive into word problems, decimals, negatives, and more to build an unshakeable skillset. Variety keeps math exciting like a fun challenge gauntlet! Interactive drills on MathBitsNotebook
  8. Remember PEMDAS - Use this classic mnemonic (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to recall how to simplify expressions before solving. A little rhyme goes a long way in keeping steps in perfect order. Sing it to memorize it! PEMDAS refresher
  9. See Real-World Connections - Two-step equations pop up everywhere: splitting a restaurant bill with tax, computing discounts, or budgeting allowance. Linking math to daily life makes concepts stick like glue! Real-world examples at Mathcation
  10. Stay Positive and Patient - Algebra is a journey, not a sprint. Each problem solved is a power-up toward tougher challenges. Keep practicing, celebrate small wins, and watch your math superpowers grow! Motivational tips from ChiliMath
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