# Select The Equivalent Equations Worksheet

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Selecting the equivalent equations means identifying the equations that are mathematically equivalent. Equivalent equations can be formed by using the properties of equality. These equations look different at first, but after simplifying them, they give the same answer. In these worksheets, students need to identify all the equations that are equivalent to the given equation.

Algebra 1
One-Variable Equations

## How Will This Worksheet on "Select the Equivalent Equations" Benefit Your Students' Learning?

• It will develop a strong understanding on equality properties and balanced equations.
• It will help to develop algebraic concepts such as solving equations, simplifying expressions, and identifying patterns.
• It improves critical thinking as analyzing and selecting equivalent equations involves critical thinking and logical reasoning.

## How to Select the Equivalent Equations?

• Examine each given equation and look for similarities and differences between it and the original equation.
• Use properties of equality to simplify each option.
• Then, select the equation which when simplified, matches with the original equation.

## Solved Example

Q. Select all of the equations below that are equivalent to:$\newline$$9 = n + -3$$\newline$Use properties of equality.$\newline$Multi-select Choices:$\newline$(A) $64 = (n + (-3)) \cdot 8$$\newline$(B) $-77 = -7(n + (-3))$$\newline$(C) $90 = (n + (-3)) \cdot 10$$\newline$(D) $63 = (n + (-3)) \cdot 7$
Solution:
1. Understand Equation: Understand the original equation.$\newline$ The original equation is $9 = n + (-3)$.$\newline$ To find equivalent equations, we can perform the same operation on both sides of the equation without changing its meaning.
2. Check Equation (A): Check equation (A) $64 = (n + (\text{–}3)) \cdot 8$.$\newline$ Divide both sides of the equation $64 = (n + (\text{–}3)) \cdot 8$ by $8$:$\newline$ $\frac{64}{8} = \frac{(n + (\text{–}3)) \cdot 8}{8}$$\newline$ $8 = n + (-3)$$\newline$ We have: $9 = n + (-3)$$\newline$ Check if $8$ equals $9$.
3. Equation (A) Comparison: Since $8$ does not equal $9$, equation (A) is not equivalent to the original equation.
4. Check Equation (B): Check equation (B) $-77 = -7(n + (-3))$.$\newline$ Divide both sides of the equation $-77 = -7(n + (-3))$ by $-7$:$\newline$ $\frac{-77}{-7} = \frac{-7(n + (-3))}{-7}$$\newline$ $11 = n + (-3)$$\newline$ We have: $9 = n + (-3)$$\newline$ Check if $11$ equals $9$.
5. Equation (B) Comparison: Since $11$ does not equal $9$, equation (B) is not equivalent to the original equation.
6. Check Equation (C): Check equation (C) $90 = (n + (–3)) \cdot 10$.$\newline$ Divide both sides of the equation $90 = (n + (–3)) \cdot 10$ by $10$:$\newline$ $\frac{90}{10} = \frac{(n + (\text{–}3)) \cdot 10}{10}$$\newline$ $9 = n + (-3)$$\newline$ We have: $9 = n + (-3)$$\newline$ Check if $9$ equals $9$.
7. Equation (C) Comparison: Since $9$ equals $9$, equation (C) is equivalent to the original equation.
8. Check Equation (D): Check equation (D) $63 = (n + (–3)) \cdot 7$.$\newline$ Divide both sides of the equation $63 = (n + (–3)) \cdot 7$ by $7$:$\newline$ $\frac{63}{7} = \frac{(n + (\text{–}3)) \cdot 7}{7}$$\newline$ $9 = n + (-3)$$\newline$ We have: $9 = n + (-3)$$\newline$ Check if $9$ equals $9$.
9. Equation (D) Comparison: Since $9$ equals $9$, equation (D) is equivalent to the original equation.

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