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Quizzes > High School Quizzes > Mathematics

Practice Quiz: 2.04 Equations Review

Ace your exam with quick equation review insights

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Equation Mastery, a challenging math trivia quiz for high school students.

Solve the equation: 2x + 3 = 11.
4
3
5
2
By subtracting 3 from both sides and dividing by 2, we find x = 4. This procedure isolates the variable and confirms the answer.
Solve the equation: 5x = 35.
7
5
6
8
Dividing both sides by 5 gives x = 7, clearly isolating the variable. This is a direct application of division.
Solve for x: x - 4 = 10.
14
16
10
12
Adding 4 to both sides yields x = 14, which is the correct solution. The equation simplifies nicely by reversing the subtraction.
Solve: x/2 = 3.
6
3
9
5
Multiplying both sides by 2 gives x = 6, isolating the variable. This is a straightforward manipulation of a fraction equation.
Solve: 3 + x = 8.
5
3
8
2
Subtracting 3 from both sides results in x = 5, making it the correct answer. This is a simple linear equation.
Solve: 2x + 4 = 3x - 2.
6
4
8
-6
By subtracting 2x from both sides and then adding 2, we isolate x and find it equals 6. Each operation is reversible and maintains the balance of the equation.
Solve: 4(x - 2) = 2x + 10.
9
8
10
11
Distribute the 4 and bring like terms together; this isolates the variable resulting in x = 9. The distribution and basic algebraic manipulation confirm the answer.
Solve: (3/4)x + 2 = 5.
4
3
6
8
Subtracting 2 from both sides isolates the fractional term, and multiplying by its reciprocal results in x = 4. This demonstrates fraction manipulation in equations.
Solve: 5 - 2(x - 1) = 3.
2
1
3
4
Expanding the parentheses and isolating x by subtracting and dividing gives x = 2. This question emphasizes applying the distributive property correctly.
Solve: (4x)/3 = 12.
9
8
10
12
Multiplying both sides by 3 and then dividing by 4 isolates x, resulting in x = 9. The equation confirms proportional reasoning.
Solve: 3(x + 4) = 2x + 20.
8
7
9
10
After expanding and rearranging terms, subtracting 2x from 3x and subtracting 12 from both sides yields x = 8. This problem reinforces distribution and combining like terms.
Solve for x: x/5 + 3 = 8.
25
20
15
30
By isolating the fractional term and multiplying by 5, we find x = 25. This manipulation underscores working with fractions in equations.
Solve: 7 - (x/2) = 4.
6
4
5
7
Subtracting and then multiplying by -2 correctly isolates x, giving us x = 6. This problem emphasizes careful sign handling in algebra.
Solve: 2(x + 5) = 3x - 1.
11
9
10
12
Expanding and rearranging the equation properly leads to the solution x = 11. Combining like terms is key to reaching the correct answer.
Solve: 6x + 2 = 3x + 20.
6
5
7
8
By subtracting 3x from both sides and isolating x, we determine x = 6. This linear equation tests the ability to simplify and balance both sides.
Solve: 3(x - 2) + 4 = 2(2x + 1) - 3.
-1
1
0
-2
After applying distribution and combining like terms, the equation simplifies to x = -1. Working through the equation step-by-step ensures the correct operation signs are maintained.
Solve: (2/3)x - (1/2)(x + 4) = 1.
18
12
10
20
Multiplying all terms by the least common denominator simplifies the fractions and leads to the solution x = 18. This problem highlights working with fractional coefficients.
Solve: 1.5x + 2.5 = 2x - 3.
11
10.5
12
13
The equation is simplified by isolating the variable term and dividing by the coefficient, leading to x = 11. This demonstrates effective handling of decimals in linear equations.
If twice a number plus 7 equals the sum of the number and 13, what is the number?
6
7
8
5
Setting up the equation from the word statement and solving it yields x = 6. This problem reinforces translating word problems into algebraic expressions.
Solve: -3(x - 2) + 2(2x - 5) = x + 1.
No solution
x = -5
x = 5
x = 0
After simplifying the equation, the variable terms cancel out, leaving an untrue statement (-4 = 1). This indicates that there is no value of x that satisfies the equation, hence no solution.
0
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Study Outcomes

  1. Identify key components and terms within equations.
  2. Simplify and solve various linear equations accurately.
  3. Verify solutions by substituting values back into equations.
  4. Analyze word problems to formulate corresponding equations.
  5. Apply algebraic techniques to isolate variables effectively.

Equations 2 Review Cheat Sheet

  1. Master the Order of Operations - PEMDAS is your secret decoder ring for complex math puzzles. By tackling Parentheses first, then Exponents, followed by Multiplication and Division (left to right), and finally Addition and Subtraction (left to right), you'll avoid the dreaded calculation headaches. Practice this rule until it's second nature, and you'll breeze through expressions with confidence. High School Math - Chapter 1
  2. Understand the Properties of Equality - Think of equations like perfectly balanced seesaws: Reflexive, Symmetric, Transitive, Substitution, Associative, Commutative, and Distributive properties are your toolkit for keeping everything level. When you wield these properties, you can reshuffle and simplify equations at will. Mastering them makes solving for x feel like child's play. High School Math - Chapter 1
  3. Apply Addition and Subtraction Properties - Adding or subtracting the same number on both sides of an equation keeps the balance intact. This straightforward trick lets you isolate variables quickly, turning complex-looking equations into simple statements. With regular practice, you'll spot the perfect moves to simplify any problem. OpenStax Prealgebra - Key Concepts
  4. Use Multiplication and Division Properties - Multiply or divide both sides of an equation by the same nonzero number, and the equality holds true. This method is essential for stripping away coefficients and honing in on the variable. It's like using a magic eraser to remove obstacles in your path. OpenStax Prealgebra - Key Concepts
  5. Solve Equations with Variables on Both Sides - When variables appear on both sides, gather like terms and shift everything to one side to simplify. This systematic approach transforms seemingly tricky equations into straightforward steps. Soon, you'll juggle terms like a pro and isolate variables without breaking a sweat. OpenStax Elementary Algebra - Key Concepts
  6. Familiarize Yourself with the Quadratic Formula - The formula x = ( - b ± √(b² - 4ac))❄(2a) is your golden ticket to solving any quadratic equation. Memorize it, understand each component, and apply it to parabolas of all shapes. With this in your arsenal, no quadratic will remain unsolved. Mathematical Scientist - Algebra Formulas
  7. Understand the Binomial Theorem - Expanding (a + b)❿ might look intimidating, but the Binomial Theorem provides a neat roadmap using combinations. Once you master this, you'll expand polynomials quickly and accurately, even for higher powers. It's like having a formulaic cheat code for polynomial growth. Mathematical Scientist - Algebra Formulas
  8. Memorize Key Algebraic Identities - Identities like (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b² are shortcuts that save time and reduce errors. Commit them to memory, and you'll transform lengthy expansions into quick mental math. These little nuggets are like cheat codes for complex expressions. Mathematical Scientist - Algebra Formulas
  9. Apply the Product of Sum and Difference - The identity (a + b)(a - b) = a² - b² is a powerful factoring tool, turning messy expressions into neat differences of squares. Use it to simplify and factor with lightning speed. Once it clicks, you'll wonder how you ever did without it. Mathematical Scientist - Algebra Formulas
  10. Develop Word-Problem Strategies - Translating real-world scenarios into algebraic equations is like cracking a secret code. Identify variables, set up equations step by step, and solve systematically to arrive at the answer. Practicing this skill boosts your analytical thinking and preps you for any math challenge. OpenStax Prealgebra - Key Concepts
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