Question

select all of the equations below that are equivalent to:
$7 - f = 7$
use properties of equality.
$7 - f - 4 = 3$ $7 - f - 2 = 5$
$7 - f - 5 = 2$ $7 - f - 3 = 4$

Explanation:

Step1: Identify original equation value

We know $7 - f = 7$.

Step2: Verify first option

Subtract 4 from both sides:
$7 - f - 4 = 7 - 4$
$\implies 7 - f - 4 = 3$
This matches the first equation.

Step3: Verify second option

Subtract 2 from both sides:
$7 - f - 2 = 7 - 2$
$\implies 7 - f - 2 = 5$
This matches the second equation.

Step4: Verify third option

Subtract 5 from both sides:
$7 - f - 5 = 7 - 5$
$\implies 7 - f - 5 = 2$
This matches the third equation.

Step5: Verify fourth option

Subtract 3 from both sides:
$7 - f - 3 = 7 - 3$
$\implies 7 - f - 3 = 4$
This matches the fourth equation.

Answer:

All of the equations are equivalent:

• $7 - f - 4 = 3$
• $7 - f - 2 = 5$
• $7 - f - 5 = 2$
• $7 - f - 3 = 4$