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Questions and Answers
What is the solution to the equation: −20 = −4x − 6x?
What is the solution to the equation: −20 = −4x − 6x?
2
What is the solution to the equation: 6x + 3 − 6x = 3?
What is the solution to the equation: 6x + 3 − 6x = 3?
Infinite Solutions
What is the simplified result of: ((−16 − (−2 + 1)) × 2) ÷ 5?
What is the simplified result of: ((−16 − (−2 + 1)) × 2) ÷ 5?
-6
What is the simplified result of: −3 ÷ 3(a + c(b + 5) − (−6 + a)) with a = 1, b = −6, and c = −4?
What is the simplified result of: −3 ÷ 3(a + c(b + 5) − (−6 + a)) with a = 1, b = −6, and c = −4?
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What is the solution to the equation: 144 = −12(x + 5)?
What is the solution to the equation: 144 = −12(x + 5)?
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What is the solution to the equation: −5(1 − 5x) + 5(−8x − 2) = −4x − 8x?
What is the solution to the equation: −5(1 − 5x) + 5(−8x − 2) = −4x − 8x?
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What is the solution to the equation: 154 = -4(8 + 6r) + 24r?
What is the solution to the equation: 154 = -4(8 + 6r) + 24r?
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What is the solution to the equation: −243 = −9(10 + x)?
What is the solution to the equation: −243 = −9(10 + x)?
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What is the simplified result of: x(z + 3) + 1 + 3 − y with x = 6, y = −5, and z = 2?
What is the simplified result of: x(z + 3) + 1 + 3 − y with x = 6, y = −5, and z = 2?
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What is the solution to the equation: a + 5 = −5a + 5?
What is the solution to the equation: a + 5 = −5a + 5?
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What is the solution to the equation: 1 = 5 + p − p?
What is the solution to the equation: 1 = 5 + p − p?
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What is the simplified result of: 7(1 + 9v) − 8(−5v − 6)?
What is the simplified result of: 7(1 + 9v) − 8(−5v − 6)?
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What is the solution to the equation: 8(k − 6) + 58 = 2(4k + 5)?
What is the solution to the equation: 8(k − 6) + 58 = 2(4k + 5)?
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What is the simplified result of: −3 × 2 × 2(−3 − 1)?
What is the simplified result of: −3 × 2 × 2(−3 − 1)?
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Translate the equation 7x = 56 into an algebraic sentence.
Translate the equation 7x = 56 into an algebraic sentence.
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Translate into an algebraic equation: u decreased by 17 is 13.
Translate into an algebraic equation: u decreased by 17 is 13.
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Translate into an algebraic equation: twice q is 8.
Translate into an algebraic equation: twice q is 8.
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Translate into an algebraic expression: the product of q and 8.
Translate into an algebraic expression: the product of q and 8.
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Translate into an algebraic expression: two less than h.
Translate into an algebraic expression: two less than h.
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Translate into an algebraic equation: twice the sum of 5 and a number.
Translate into an algebraic equation: twice the sum of 5 and a number.
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What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 3x + 1 = 10?
What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 3x + 1 = 10?
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What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 4x = x × 4?
What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 4x = x × 4?
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What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 2 = x - 4?
What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 2 = x - 4?
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Study Notes
Equation Solutions
- To solve −20 = −4x − 6x, the solution is x = 2.
- The equation 6x + 3 − 6x = 3 leads to an infinite number of solutions.
- For 144 = −12(x + 5), the solution is x = -17.
- The equation −243 = −9(10 + x) results in x = 17.
- In the case of 8(k − 6) + 58 = 2(4k + 5), there are infinite solutions.
- The equation 3x + 1 = 10 with the domain (0, 1, 2, 3, 4, 5, 6) gives the solution set {3}.
- The equation 4x = x × 4 also provides the entire domain {0, 1, 2, 3, 4, 5, 6} as solutions.
- For the equation 2 = x - 4, the solution is x = 6.
Simplifications
- Simplifying ((−16 − (−2 + 1)) × 2) ÷ 5 results in -6.
- Simplifying −3 ÷ 3(a + c(b + 5) − (−6 + a)) using a = 1, b = −6, and c = −4 yields -10.
- For 7(1 + 9v) − 8(−5v − 6), simplification leads to 55 + 103v.
- The expression −3 × 2 × 2(−3 − 1) simplifies to 48.
Algebraic Translations
- The equation 7x = 56 translates to "the product of x and 7 is fifty-six".
- "u decreased by 17 is 13" translates into algebraic form as u - 17 = 13.
- The phrase "twice q is 8" translates to the equation 2q = 8.
- "The product of q and 8" becomes the expression 8q.
- "Two less than h" translates to h - 2.
- "Twice the sum of 5 and a number" is translated into the expression 2(5 + n).
Special Cases
- The equation −5(1 − 5x) + 5(−8x − 2) = −4x − 8x produces x = -5.
- The equation 154 = -4(8 + 6r) + 24r results in no solution.
- The equation 1 = 5 + p − p also yields no solution.
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Description
This quiz explores various methods for solving algebraic equations, simplifying expressions, and translating verbal statements into algebraic equations. Test your understanding of equations, simplifications, and translations to enhance your algebra skills.
