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Questions and Answers
What is the solution to the equation $x - 5 = -13$?
What is the solution to the equation $x - 5 = -13$?
x = -8
What is the solution to the equation $-8 = n - (-4)$?
What is the solution to the equation $-8 = n - (-4)$?
n = -12
Are the equations $17x = 85$ and $x = 5$ equivalent?
Are the equations $17x = 85$ and $x = 5$ equivalent?
True
Are the equations $-16x = 48$ and $x = 3$ equivalent?
Are the equations $-16x = 48$ and $x = 3$ equivalent?
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What is the solution to the equation $\frac{b}{2} = 14$?
What is the solution to the equation $\frac{b}{2} = 14$?
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What is the solution to the equation $14x + 3x - 40 = 11$?
What is the solution to the equation $14x + 3x - 40 = 11$?
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Write and solve an equation to find the three consecutive integers that sum to 417.
Write and solve an equation to find the three consecutive integers that sum to 417.
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What is the solution to the equation $3x - 8 = -3x + 4$?
What is the solution to the equation $3x - 8 = -3x + 4$?
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If a gym charges $10 per hour as a non-member and $300 plus $4 per hour as a member, how many hours must you play as a non-member to justify becoming a member?
If a gym charges $10 per hour as a non-member and $300 plus $4 per hour as a member, how many hours must you play as a non-member to justify becoming a member?
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How wide can each picture be if you are designing a web page with 4 pictures, a width of 640, margins of 24, and 16 in between each picture?
How wide can each picture be if you are designing a web page with 4 pictures, a width of 640, margins of 24, and 16 in between each picture?
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What is the solution to the equation $-15x + 73 = 26$?
What is the solution to the equation $-15x + 73 = 26$?
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What is the solution to the equation $1.5x + 7.4 = -1.8x - 6.9$?
What is the solution to the equation $1.5x + 7.4 = -1.8x - 6.9$?
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How can you rewrite the equation $6.2x + 4.5 = 3.8x + 7.9$ by multiplying by 10?
How can you rewrite the equation $6.2x + 4.5 = 3.8x + 7.9$ by multiplying by 10?
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How do you solve for $b_1$ in the equation $A = \frac{1}{2}h(b_1 + b_2)$?
How do you solve for $b_1$ in the equation $A = \frac{1}{2}h(b_1 + b_2)$?
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Rewrite the equation $3x + 5y = 15$ so that y is a function of x.
Rewrite the equation $3x + 5y = 15$ so that y is a function of x.
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What is the unit rate for 3 tablespoons for 1.5 servings?
What is the unit rate for 3 tablespoons for 1.5 servings?
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How many tablespoons are in 15 teaspoons, knowing that 1 tablespoon equals 3 teaspoons?
How many tablespoons are in 15 teaspoons, knowing that 1 tablespoon equals 3 teaspoons?
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What percentage of people were in favor if 159 out of 350 were?
What percentage of people were in favor if 159 out of 350 were?
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Study Notes
Solving Equations
- For the equation x - 5 = -13, the solution is x = -8.
- Solving the expression -8 = n - (-4) results in n = -12.
- The equations 17x = 85 and x = 5 are equivalent, confirming the solution is consistent.
- In contrast, -16x = 48 and x = 3 are not equivalent.
Algebraic Solutions
- Solving b/2 = 14 gives b = 28.
- The equation 14x + 3x - 40 = 11 simplifies to x = 3.
Consecutive Integers Problem
- The sum of three consecutive integers can be expressed as x + (x + 1) + (x + 2) = 417, leading to x = 138.
Additional Equations
- The equation 3x - 8 = -3x + 4 simplifies to find x = 2.
- A financial problem described by 10h = 300 + 4h results in h = 50 hours for nonmembers to consider membership.
Geometry and Design
- For a webpage with 4 pictures within a width of 640, accounting for margins and spacing leads to each picture being 136 in width.
- The equation -15x + 73 = 26 resolves to x = 3.13.
More Algebraic Manipulations
- The equation 1.5x + 7.4 = -1.8x - 6.9 simplifies to x = -4.33.
- An equivalent equation of 6.2x + 4.5 = 3.8x + 7.9 after multiplying by 10 is 62x + 45 = 38x + 79.
Geometry Formula
- Solving for b1 in the formula A = 1/2h(b1 + b2) results in the expression b1 = (2A/h) - b2.
Functions
- The equation 3x + 5y = 15 can be rewritten to express y as a function of x: y = 3 - (3/5)x.
Unit Rate and Conversion
- The unit rate for 3 tablespoons serving 1.5 servings is calculated to be 2.
- Converting 15 teaspoons into tablespoons results in 5 (1 tablespoon = 3 teaspoons).
Percent Calculation
- To find the percentage, 159 people in favor out of 350 result in approximately 45%.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz features flashcards focused on solving equations and determining the equivalence of different algebraic expressions in Algebra 1 Unit 3. Test your skills on manipulating and solving various algebraic problems.
