Select all of the equations below that are equivalent to: –14 = f + 32 Use properties of equality. Multi-select Choices: (A)–2 · –14 = –2f + –64 (B)–2 · –14 = –2f + –68 (C)–3 · –14 = –3f + –96 (D)–3 · –14 = –3f + –99

Apply Operation: To determine if the equations are equivalent, we need to apply the same operation to both sides of the original equation and see if we get the equations in the choices. Let's start with choice (A): Multiply both sides of the original equation by –2. Calculation: (–2) * (–14) = (–2) * (f + 32)Check Choice (A): Now, let's simplify the right side of the equation. Calculation: 28 = –2f – 64Check Choice (B): We can see that the result matches choice (A). So, choice (A) is equivalent to the original equation.Check Choice (C): Next, let's check choice (B) by multiplying both sides of the original equation by –2. Calculation: (–2) * (–14) = (–2) * (f + 32)Check Choice (D): Simplify the right side of the equation. Calculation: 28 = –2f – 64We can see that the result does not match choice (B) because choice (B) has –68 instead of –64. So, choice (B) is not equivalent to the original equation.Now, let's check choice (C) by multiplying both sides of the original equation by –3. Calculation: (–3) * (–14) = (–3) * (f + 32)Simplify the right side of the equation. Calculation: 42 = –3f – 96We can see that the result matches choice (C). So, choice (C) is equivalent to the original equation.Finally, let's check choice (D) by multiplying both sides of the original equation by –3. Calculation: (–3) * (–14) = (–3) * (f + 32)Simplify the right side of the equation. Calculation: 42 = –3f – 96We can see that the result does not match choice (D) because choice (D) has –99 instead of –96. So, choice (D) is not equivalent to the original equation.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Select all of the equations below that are equivalent to: $\newline$ $-14 = f + 32$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $-2 \cdot -14 = -2f + -64$ $\newline$ (B) $-2 \cdot -14 = -2f + -68$ $\newline$ (C) $-3 \cdot -14 = -3f + -96$ $\newline$ (D) $-3 \cdot -14 = -3f + -99$

View step-by-step help

Home

Math Problems

Algebra 1

Identify equivalent equations

Full solution

Q. Select all of the equations below that are equivalent to:

\newline

-14 = f + 32

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

-2 \cdot -14 = -2f + -64

\newline

(B)

-2 \cdot -14 = -2f + -68

\newline

(C)

-3 \cdot -14 = -3f + -96

\newline

(D)

-3 \cdot -14 = -3f + -99

Apply Operation: To determine if the equations are equivalent, we need to apply the same operation to both sides of the original equation and see if we get the equations in the choices. $\newline$ Let's start with choice (A): Multiply both sides of the original equation by $–2$ . $\newline$ Calculation: $(–2) \times (–14) = (–2) \times (f + 32)$
Check Choice (A): Now, let's simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$
Check Choice (B): We can see that the result matches choice $(A)$ . So, choice $(A)$ is equivalent to the original equation.
Check Choice (C): Next, let's check choice (B) by multiplying both sides of the original equation by $–2$ . $\newline$ Calculation: $(–2) \times (–14) = (–2) \times (f + 32)$
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$ We can see that the result does not match choice (B) because choice (B) has $-68$ instead of $-64$ . $\newline$ So, choice (B) is not equivalent to the original equation.
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$ We can see that the result does not match choice (B) because choice (B) has $-68$ instead of $-64$ . $\newline$ So, choice (B) is not equivalent to the original equation.Now, let's check choice (C) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$ We can see that the result does not match choice (B) because choice (B) has $-68$ instead of $-64$ . $\newline$ So, choice (B) is not equivalent to the original equation.Now, let's check choice (C) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$ Simplify the right side of the equation. $\newline$ Calculation: $42 = -3f - 96$
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$ We can see that the result does not match choice (B) because choice (B) has $-68$ instead of $-64$ . $\newline$ So, choice (B) is not equivalent to the original equation.Now, let's check choice (C) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$ Simplify the right side of the equation. $\newline$ Calculation: $42 = -3f - 96$ We can see that the result matches choice (C). $\newline$ So, choice (C) is equivalent to the original equation.
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$ We can see that the result does not match choice (B) because choice (B) has $-68$ instead of $-64$ . $\newline$ So, choice (B) is not equivalent to the original equation.Now, let's check choice (C) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$ Simplify the right side of the equation. $\newline$ Calculation: $42 = -3f - 96$ We can see that the result matches choice (C). $\newline$ So, choice (C) is equivalent to the original equation.Finally, let's check choice (D) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$ We can see that the result does not match choice (B) because choice (B) has $-68$ instead of $-64$ . $\newline$ So, choice (B) is not equivalent to the original equation.Now, let's check choice (C) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$ Simplify the right side of the equation. $\newline$ Calculation: $42 = -3f - 96$ We can see that the result matches choice (C). $\newline$ So, choice (C) is equivalent to the original equation.Finally, let's check choice (D) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$ Simplify the right side of the equation. $\newline$ Calculation: $42 = -3f - 96$
Check Choice (D): Simplify the right side of the equation. $\newline$ Calculation: $28 = -2f - 64$ We can see that the result does not match choice (B) because choice (B) has $-68$ instead of $-64$ . $\newline$ So, choice (B) is not equivalent to the original equation.Now, let's check choice (C) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$ Simplify the right side of the equation. $\newline$ Calculation: $42 = -3f - 96$ We can see that the result matches choice (C). $\newline$ So, choice (C) is equivalent to the original equation.Finally, let's check choice (D) by multiplying both sides of the original equation by $-3$ . $\newline$ Calculation: $(-3) \times (-14) = (-3) \times (f + 32)$ Simplify the right side of the equation. $\newline$ Calculation: $42 = -3f - 96$ We can see that the result does not match choice (D) because choice (D) has $-99$ instead of $-68$ $0$ . $\newline$ So, choice (D) is not equivalent to the original equation.

Full solution

More problems from Identify equivalent equations

Related topics