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Quizzes > High School Quizzes > Mathematics

Unit 4 Lesson 7 Practice Quiz Answers

Master key lessons with clear, step-by-step guides

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art representing a trivia quiz for high school algebra students to review Unit 4 concepts.

Solve the equation: 2x = 10.
x = 5
x = 10
x = 2
x = 4
Dividing both sides of the equation by 2 gives x = 10/2, which is 5. This is the correct solution for the equation.
Simplify the expression: x + x.
2x
x²
x
2
Since x is added to x, you combine like terms to get 2x. This is a basic application of combining similar terms.
Solve for x: x + 3 = 7.
4
3
7
10
Subtracting 3 from both sides of the equation yields x = 4. This simple operation isolates the variable x.
Find the value of y in the equation: 3y = 12.
4
3
12
6
Dividing both sides by 3 gives y = 12/3, which simplifies to y = 4. This basic division isolates y correctly.
Which of the following is a like term with 5x?
7x
5
x + 5
5y
Like terms have the same variable part. '7x' shares the variable x with 5x, making it a like term, while the other options do not.
Solve the equation: 3x - 5 = 2x + 4.
x = 9
x = -9
x = 1
x = -1
Subtracting 2x from both sides yields x - 5 = 4, and adding 5 to both sides results in x = 9. This step-by-step isolation shows the correct solution.
Solve for y: 2(y - 3) = y + 4.
y = 10
y = 7
y = 4
y = -10
Distributing on the left gives 2y - 6, and setting the equation as 2y - 6 = y + 4 leads to y = 10 after subtracting y and adding 6. This is the correct solution.
Simplify the expression: 4x + 3 - 2x + 5.
2x + 8
6x + 8
2x - 2
4x + 8
Combine like terms by subtracting 2x from 4x to get 2x and adding 3 and 5 to get 8, resulting in 2x + 8. This is the properly simplified expression.
Solve the inequality: 2x + 1 < 7.
x < 3
x > 3
x ≤ 3
x = 3
Subtracting 1 yields 2x < 6, and dividing by 2 gives x < 3. This is the correct interpretation of the inequality.
Given that 3x = 9, what is the value of x²?
9
3
6
27
Dividing 3x = 9 by 3 gives x = 3, and squaring 3 results in x² = 9. This is a straightforward substitution and squaring process.
Solve for z in the equation: 5(z + 2) = 3z + 14.
2
4
3
-2
Expanding gives 5z + 10 = 3z + 14. Subtracting 3z and then subtracting 10 provides 2z = 4, leading to z = 2 after division.
Simplify and factor the expression: 2x² + 4x.
2x(x + 2)
2(x + 2)
x(2x + 4)
2x² + 2
The common factor in both terms is 2x, which when factored out yields 2x(x + 2). This is the appropriate factorization for the expression.
Solve for x in the equation: (1/2)x + 3 = 7.
8
7
10
4
Subtracting 3 from both sides gives (1/2)x = 4, and multiplying both sides by 2 results in x = 8. This is the correct solution.
What property allows the term a + b to be rewritten as b + a?
Commutative property
Associative property
Distributive property
Identity property
The commutative property of addition states that the order of the terms does not affect the sum. Thus, a + b can be rearranged as b + a.
Evaluate the expression: 2(3x - 4) for x = 5.
22
26
18
30
Substituting x = 5 gives 2(15 - 4) = 2(11), which equals 22. This calculation confirms the correct value of the expression.
Solve the equation: 2(3x - 2) = 4x + 10.
x = 7
x = 6
x = 8
x = 5
Expanding the left-hand side results in 6x - 4, and setting it equal to 4x + 10 gives 2x = 14. Dividing by 2 confirms that x = 7.
Solve the system: x + y = 10 and x - y = 2. What are the values of x and y?
x = 6, y = 4
x = 4, y = 6
x = 8, y = 2
x = 2, y = 8
By adding the two equations, we eliminate y to obtain 2x = 12, so x = 6. Substituting back into x + y = 10 gives y = 4, which is the correct solution.
Factor the expression completely: x² - 16.
(x - 4)(x + 4)
(x - 16)(x + 1)
(x - 8)(x + 2)
(x - 2)(x + 8)
The expression x² - 16 is a difference of squares and factors into (x - 4)(x + 4). This is a standard algebraic identity used for factoring.
Solve the equation: (x/3) + (x/4) = 7.
12
7
14
10
Finding a common denominator gives (7x/12) = 7, so multiplying both sides by 12 and then dividing by 7 results in x = 12. This is the correct approach.
Solve for x: 2 - 3(2 - x) = 4x + 1.
x = -5
x = 5
x = -3
x = 3
Expanding the left-hand side yields 2 - 6 + 3x which simplifies to 3x - 4. Setting this equal to 4x + 1 and solving for x produces x = -5, the correct solution.
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Study Outcomes

  1. Analyze exam-style algebra questions to identify problem-solving strategies.
  2. Synthesize key algebraic concepts to approach and solve equations effectively.
  3. Apply problem-solving techniques to address diverse practice quiz problems.
  4. Evaluate performance to identify strengths and areas for further review.

Unit 4 Lesson 7 Practice Prob. Answer Key Cheat Sheet

  1. Standard Form Fundamentals - The standard form of a quadratic equation, ax² + bx + c = 0, is your launchpad for solving quadratics like a pro. Recognizing how each coefficient shapes the graph makes choosing the right solution method a breeze. Algebra 1 Unit 4 Review Answer Key
  2. Factoring, Completing the Square & the Formula - There's more than one way to crack a quadratic! Learn how to pull roots by factoring, convert to a perfect square, or simply apply the quadratic formula for instant results. Mastering all three keeps you flexible when homework throws curveballs. Algebra 1 Unit 4 Review Answer Key
  3. Graphing Quadratics - Plotting a parabola means finding its vertex, axis of symmetry, and opening direction - your roadmap to visualizing quadratic behavior. Spotting these key features turns abstract equations into colorful, easy-to-read curves. Plus, a quick sketch can double‑check your algebraic answers! Algebra 1 Unit 4 Review Answer Key
  4. Forms of Quadratics - Quadratics come in standard, vertex, and factored forms, each offering unique insights: standard shows coefficients, vertex reveals the peak, and factored gives the roots. Switching between them is like having different lenses to examine the same function. Practice transforming one form into another to master quadratic versatility. Algebra 1 Unit 4 Review Answer Key
  5. Systems with Quadratics - Combining quadratics with lines or other curves tests your problem‑solving chops in algebraic and graphical ways. Finding intersection points reveals real‑world solutions, from projectile motion to optics. Sharpen both algebraic elimination and graph‑sketching skills to ace these mixed systems. Algebra 1 Unit 4 Review Answer Key
  6. Discriminant Decisions - The discriminant (b² - 4ac) is your quick-check tool for root reality: positive means two distinct real roots, zero means one real root, and negative means complex pairs. No need to race through the whole formula - just compute b² - 4ac and know what to expect. It's like having a spoiler alert for solutions! Algebra 1 Unit 4 Review Answer Key
  7. Exponential Growth & Decay - Exponential functions model everything from viral TikTok trends to radioactive decay. Understand the formula y = a·b^x, learn how the base b drives rapid rises or falls, and explore real‑world scenarios like interest calculations. These concepts make math feel alive - and surprisingly relevant. Algebra Two Unit 4 Guide
  8. Logarithmic Inverses - Logarithms flip exponent rules upside down, letting you solve for unknown exponents in equations like b^x = y. Get comfortable converting between log and exponential forms and graphing log curves to see their slowly increasing shape. Logs are your secret weapon for cracking exponent puzzles. Algebra Two Unit 4 Guide
  9. Log Properties Mastery - The product, quotient, and power rules let you simplify complex log expressions in seconds. Combine logs into single terms or expand them into bite‑sized pieces to solve equations quickly. Nailing these rules saves time and keeps your work neat on tests! Algebra Two Unit 4 Guide
  10. Real‑World Exponential & Log Problems - Apply your skills to compound interest, population growth, and pH calculations to see how exponentials and logs drive real data. These applications turn abstract formulas into practical tools you'll use outside the classroom. Practice a few word problems and impress everyone with your math‑in‑action prowess! Algebra Two Unit 4 Guide
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