Solve for w..

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:

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

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

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:

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

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

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:

\[ \boxed{2.00} \]

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

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:

\[ \boxed{4} \]

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

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:

\[ \boxed{10} \]

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.

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.