Identify the first step in solving this equation for x : 7(x − 8) = 49 . Multiply both sides by 7. Add 8 to both sides. Divide both sides by 7. Divide only the left side by 7.

Answer 1

The first step in solving the equation \( 7(x - 8) = 49 \) is to divide both sides by 7. This will simplify the equation and isolate the term with \( x \).

So, the correct first step is: Divide both sides by 7.

Answer 2

Identify the second step in solving this equation for y : −3(y + 6) = 21 .
Divide both sides by −3 .
Divide both sides by 6.
Subtract 6 from both sides.
Add 6 to both sides.

Answer 3

To solve the equation \( -3(y + 6) = 21 \), the first step would be to divide both sides by -3. This simplifies the equation to \( y + 6 = -7 \).

Now, the second step would be to subtract 6 from both sides to isolate \( y \).

So, the correct second step is: Subtract 6 from both sides.

Answer 4

For which equation is the order of steps to first divide both sides by 6 and then to add 8 to both sides?
6(x − 8) = 48
6(x + 8) = 48
8(x − 6) = 48
6x − 8 = 48

Answer 5

To find an equation for which the steps involve first dividing both sides by 6 and then adding 8 to both sides, we can analyze each given equation.

1. \( 6(x - 8) = 48 \):

   • Dividing by 6 gives: \( x - 8 = 8 \)
   • Adding 8 gives: \( x = 16 \)

2. \( 6(x + 8) = 48 \):

   • Dividing by 6 gives: \( x + 8 = 8 \)
   • Adding 8 results in \( x + 8 = 8\) (no addition step needed).

3. \( 8(x - 6) = 48 \):

   • Dividing by 8 gives: \( x - 6 = 6 \)
   • Adding 8 is not applicable here.

4. \( 6x - 8 = 48 \):

   • Adding 8 first leads to: \( 6x = 56 \)
   • Then dividing by 6.

Looking closely, the only equation where the first operation is to divide by 6 and the second operation involves adding 8 is:

\( 6(x - 8) = 48 \).

So, this is the correct equation.

Answer 6

For which equation is the order of steps to first divide both sides by 2 and then to subtract 10 from both sides?
10(x + 2) = 16
2(x + 10) = 16
2x + 10 = 16
2(x − 10) = 16

Answer 7

To determine which equation allows for the order of steps to first divide both sides by 2 and then subtract 10 from both sides, let's analyze each equation:

1. \( 10(x + 2) = 16 \):

   • Dividing by 10: \( x + 2 = \frac{16}{10} \) (instead of dividing by 2).

2. \( 2(x + 10) = 16 \):

   • Dividing by 2: \( x + 10 = 8 \)
   • Subtracting 10 does not apply as you would subtract the 10 from \( x + 10 = 8 \).

3. \( 2x + 10 = 16 \):

   • Subtracting 10 first: \( 2x = 6 \)
   • Then dividing by 2 afterward.

4. \( 2(x - 10) = 16 \):

   • Dividing by 2: \( x - 10 = 8 \)
   • Adding or subtracting does not apply afterwards based on the order specified.

Now, we can conclude that the only equation that allows you to first divide by 2 and then subtract (in this case, subtracting 10 logically results in a step after dividing by 2) is:

\( 2(x + 10) = 16 \).

Thus, that equation meets the criteria you specified.

Answer 8

What is the solution of the equation −4(z + 12) = 36 when solving for z ?
24
−6
21
−21

Answer 9

To solve the equation \( -4(z + 12) = 36 \) for \( z \), follow these steps:

1. Divide both sides by -4: \[ z + 12 = \frac{36}{-4} \] \[ z + 12 = -9 \]

2. Subtract 12 from both sides: \[ z = -9 - 12 \] \[ z = -21 \]

Therefore, the solution to the equation \( -4(z + 12) = 36 \) is \( z = -21 \).

Thus, the correct answer is −21.