QuestionFind all equations equivalent to: $-62 = r + s$ . Consider the following options.

Studdy Solution

STEP 1

Assumptions1. The given equation is $-62 = r + s$ . We are looking for equivalent equations using properties of equality

STEP 2

The property of equality we'll use is the multiplication property, which states that if you multiply both sides of an equation by the same number, the equation remains equivalent.

STEP 3

Let's start by checking the first equation $-33 = \frac{r + s}{2}$ . To see if it's equivalent to the original equation, we need to multiply both sides by2.
$-33 \times2 = \frac{r + s}{2} \times2$

STEP 4

Calculate the left side and simplify the right side.
$-66 = r + s$

STEP 5

This equation is not equivalent to the original equation $-62 = r + s$ . So, the first equation is not equivalent.

STEP 6

Now, let's check the second equation $33 = \frac{r + s}{-2}$ . Again, we multiply both sides by -2.
$33 \times -2 = \frac{r + s}{-2} \times -2$

STEP 7

Calculate the left side and simplify the right side.
$-66 = r + s$

STEP 8

This equation is not equivalent to the original equation $-62 = r + s$ . So, the second equation is not equivalent.

STEP 9

Now, let's check the third equation $-3 = \frac{r + s}{31}$ . We multiply both sides by31.
$-3 \times31 = \frac{r + s}{31} \times31$

STEP 10

Calculate the left side and simplify the right side.
$-93 = r + s$

STEP 11

This equation is not equivalent to the original equation $-62 = r + s$ . So, the third equation is not equivalent.

STEP 12

Finally, let's check the fourth equation $-31 = \frac{r + s}{2}$ . We multiply both sides by2.
$-31 \times2 = \frac{r + s}{2} \times2$

STEP 13

Calculate the left side and simplify the right side.
$-62 = r + s$

STEP 14

This equation is equivalent to the original equation $-62 = r + s$ . So, the fourth equation is equivalent.
In conclusion, only the fourth equation $-31 = \frac{r + s}{2}$ is equivalent to the original equation $-62 = r + s$ .

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