Algebra Equivalence and Solutions Quiz

What is equivalent to -16? Select all that apply.

What is equivalent to x - 3? Select all that apply.

Which expression is not equivalent to the others?

Which of the following equations have a solution of -3? Select all that apply.

What is the first incorrect step in the solution of 1/5(10 - 15y) = 2y - 13?

Which is a correct first step to solve the equation 2 - 3(c - 7) = c + 5? Select all that apply.

Which is NOT a correct first step to solve 3x + 5 = 2x - 4?

Which of the following would give you 'No Solution'? Select all that apply.

The length of a rectangle is 3 inches shorter than the width. Which expressions model the perimeter of the rectangle? Select all that apply.

The length of a rectangle is 4ft more than three times the width. If the perimeter is 40ft, what are the dimensions of the rectangle?

Which equation finds W, given l and h in the volume formula V = lwh?

Which rule matches the table of values: X | -2 -1 0 1 2, Y | -3 0 7 12 9?

Which rule matches the table of values: X | -2 -1 0 1 2, Y | -7 0 1 2 9?

Which ordered pair matches the rule y = -2x + 3?

Which ordered pair could NOT be part of a function that includes (-3, 3), (-2, 2), (-1, 1), (0, 0), and (1, -1)?

Equivalent Expressions

For -16, select equivalents:
- A, B, C, D, E all are equivalent expressions that evaluate to -16.

Expressions Equivalent to x - 3

To find equivalents to x - 3, select:
- A, D, E are valid expressions equivalent to x - 3.

Non-Equivalent Expression

Among the following, C is not equivalent to the others:
- A evaluates to 3(2t - 4)
- B evaluates to -(12 - 6t)
- D evaluates to 6(-2 + t)

Solutions to Equations

Equations with a solution of -3 include:
- A, B, C, D are valid equations that equal -3.

Incorrect Step in Equation Solution

Identify the first incorrect step in solving:
- B is the first incorrect step in 1/5 (10 - 15y) = 2y - 13.

Steps to Solve an Equation

Correct initial steps for solving 2 - 3(c - 7) = c + 5 are:
- A is a valid first step.

Incorrect Methods to Solve

Non-correct approaches for solving 3x + 5 = 2x - 4:
- A is not a valid method.

Conditions for "No Solution"

To yield "No Solution," select from:
- B, C, F are the equations leading to no valid solution.

Perimeter of a Rectangle

For a rectangle with a length of 3 inches shorter than the width:
- A and B correctly model the perimeter of the rectangle.

Dimensions of a Rectangle

Length and width satisfying perimeter:
- A gives correct dimensions: Length = 16 ft, width = 4 ft.

Volume Formula

Volume V = lwh: to find W when given l and h, rewrite as:
- W = V / (l * h).

Rules Matching Tables

For the table with X: -2, -1, 0, 1, 2 and Y: -3, 0, 7, 12, 9:
- B (y = 5x + 7) matches the data.

Another Rule Matching Table

For the table with X: -2, -1, 0, 1, 2 and Y: -7, 0, 1, 2, 9:
- D (y = x^3 + 1) correctly matches the data points.

Ordered Pair for Given Rule

Ordered pairs that satisfy y = -2x + 3:
- A (-1, -1) is an example that fits.

Possible Function Pair

Among the options, D (0, 5) could not be part of a function given the preceding points: (-3, 3), (-2, 2), (-1, 1), (0, 0), (1, -1).

Test your understanding of equivalent expressions and solutions in algebra. This quiz covers topics such as recognizing equivalent forms, identifying incorrect methods, and solving equations. Challenge yourself with various scenarios to enhance your skills in algebraic reasoning.