Algebra Equation Solutions and Simplifications

Questions and Answers

What is the solution to the equation: −20 = −4x − 6x?

What is the solution to the equation: 6x + 3 − 6x = 3?

Infinite Solutions

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?

-10 Signup and view all the answers

What is the solution to the equation: 144 = −12(x + 5)?

{-17} Signup and view all the answers

What is the solution to the equation: −5(1 − 5x) + 5(−8x − 2) = −4x − 8x?

-5 Signup and view all the answers

What is the solution to the equation: 154 = -4(8 + 6r) + 24r?

No Solution Signup and view all the answers

What is the solution to the equation: −243 = −9(10 + x)?

{17} Signup and view all the answers

What is the simplified result of: x(z + 3) + 1 + 3 − y with x = 6, y = −5, and z = 2?

39 Signup and view all the answers

What is the solution to the equation: a + 5 = −5a + 5?

0 Signup and view all the answers

What is the solution to the equation: 1 = 5 + p − p?

No Solution Signup and view all the answers

What is the simplified result of: 7(1 + 9v) − 8(−5v − 6)?

55 + 103v Signup and view all the answers

What is the solution to the equation: 8(k − 6) + 58 = 2(4k + 5)?

Infinite Solutions Signup and view all the answers

What is the simplified result of: −3 × 2 × 2(−3 − 1)?

48 Signup and view all the answers

Translate the equation 7x = 56 into an algebraic sentence.

the product of x and 7 is fifty-six Signup and view all the answers

Translate into an algebraic equation: u decreased by 17 is 13.

u - 17 = 13 Signup and view all the answers

Translate into an algebraic equation: twice q is 8.

2q = 8 Signup and view all the answers

Translate into an algebraic expression: the product of q and 8.

8q Signup and view all the answers

Translate into an algebraic expression: two less than h.

h - 2 Signup and view all the answers

Translate into an algebraic equation: twice the sum of 5 and a number.

2(5 + n) Signup and view all the answers

What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 3x + 1 = 10?

{3} Signup and view all the answers

What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 4x = x × 4?

{0, 1, 2, 3, 4, 5, 6} Signup and view all the answers

What is the solution if the domain of x is (0, 1, 2, 3, 4, 5, 6); 2 = x - 4?

{6} Signup and view all the answers

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.