Question

Solve for w..

15w+3w+19=−17

(1 point)
Responses

w = 4
w = 4

w = 2
w = 2

w = -3
w = -3

w = -2

Answer 1

Simplify the expression.

(6x−10)−(2x+12)

(1 point)
Responses

4x+2
4 x plus 2

8x−2
8 x minus 2

8x−22
8 x minus 22

4x−22

Answer 2

Jenny bought 6 cookies and 6 cupcakes at the bakery. The cookies were $1.50 each, but she cannot remember how much each cupcake was. She paid $21 total. How much was each cupcake?(1 point)
Responses

$1.50
$1.50

$12.00
$12.00

$2.00
$2.00

$2.50

Answer 3

Half the sum of a number and 26 is 15. What is the number?(1 point)
Responses

-11
-11

4
4

5.5
5.5

-22

Answer 4

Four times the difference of a number and 7 is 12. What is the number?(1 point)
Responses

10
10

-4
-4

16
16

20

Answer 5

What is the first step in solving the equation

3=6y+9


(1 point)
Responses

Divide both sides by 3.
Divide both sides by 3.

Subtract 3 from both sides.
Subtract 3 from both sides.

Add 9 to both sides.
Add 9 to both sides.

Subtract 9 from both sides.

Answer 6

To solve the equation \( 15w + 3w + 19 = -17 \), we first combine like terms:

\[
15w + 3w = 18w
\]

So the equation becomes:

\[
18w + 19 = -17
\]

Next, we isolate \( 18w \) by subtracting \( 19 \) from both sides:

\[
18w + 19 - 19 = -17 - 19
\]

This simplifies to:

\[
18w = -36
\]

Now, we solve for \( w \) by dividing both sides by \( 18 \):

\[
w = \frac{-36}{18} = -2
\]

Thus, the solution is:

\[
\boxed{w = -2}
\]

Answer 7

To simplify the expression \((6x - 10) - (2x + 12)\), we first distribute the negative sign through the second parentheses:

\[
(6x - 10) - (2x + 12) = 6x - 10 - 2x - 12
\]

Next, we combine like terms:

1. Combine the \(x\) terms: \(6x - 2x = 4x\)
2. Combine the constant terms: \(-10 - 12 = -22\)

Putting it all together, we get:

\[
4x - 22
\]

Thus, the simplified expression is:

\[
\boxed{4x - 22}
\]

Answer 8

Let's denote the cost of each cupcake as \( x \).

Jenny bought 6 cookies and 6 cupcakes. The total cost for the cookies is:

\[
6 \text{ cookies} \times 1.50 \text{ dollars/cookie} = 9 \text{ dollars}
\]

The total amount Jenny paid for the cupcakes is:

\[
6 \text{ cupcakes} \times x \text{ dollars/cupcake} = 6x \text{ dollars}
\]

According to the problem, Jenny paid a total of $21, so we can set up the following equation:

\[
9 + 6x = 21
\]

Now, we will solve for \( x \):

1. Subtract 9 from both sides:

\[
6x = 21 - 9 \\
6x = 12
\]

2. Divide both sides by 6:

\[
x = \frac{12}{6} = 2
\]

Thus, the cost of each cupcake is:

\[
\boxed{2.00}
\]

Answer 9

Let's denote the unknown number as \( x \).

According to the problem, half the sum of this number and 26 is 15. We can write this as an equation:

\[
\frac{x + 26}{2} = 15
\]

Now, to eliminate the fraction, we multiply both sides of the equation by 2:

\[
x + 26 = 30
\]

Next, we isolate \( x \) by subtracting 26 from both sides:

\[
x = 30 - 26
\]
\[
x = 4
\]

Therefore, the number is:

\[
\boxed{4}
\]

Answer 10

Let's denote the unknown number as \( x \).

According to the problem, four times the difference of this number and 7 is 12. We can write this as an equation:

\[
4(x - 7) = 12
\]

Now, we solve for \( x \):

1. Divide both sides by 4 to isolate the expression inside the parentheses:

\[
x - 7 = \frac{12}{4} \\
x - 7 = 3
\]

2. Next, add 7 to both sides to solve for \( x \):

\[
x = 3 + 7 \\
x = 10
\]

Therefore, the number is:

\[
\boxed{10}
\]

Answer 11

To solve the equation \( 3 = 6y + 9 \), the first step is to isolate the term involving \( y \).

To do that, we want to eliminate the \( 9 \) from the right side of the equation. The appropriate first step would be to **subtract 9 from both sides** of the equation.

So the correct response is:

**Subtract 9 from both sides.**