Which of the following equations have a solution of z = 3 ?

Question

select the TWO correct equations.
9z − 5 = 22
9z + 22 = 26
5z + 40 = 62
54 − 8z = 30

Answer 1

To determine which equations have a solution of \( z = 3 \), we can substitute \( z = 3 \) into each equation and check if the equations hold true.

1. Equation: \( 9z - 5 = 22 \) \[ 9(3) - 5 = 27 - 5 = 22 \quad \text{(True)} \]

2. Equation: \( 9z + 22 = 26 \) \[ 9(3) + 22 = 27 + 22 = 49 \quad \text{(Not true)} \]

3. Equation: \( 5z + 40 = 62 \) \[ 5(3) + 40 = 15 + 40 = 55 \quad \text{(Not true)} \]

4. Equation: \( 54 - 8z = 30 \) \[ 54 - 8(3) = 54 - 24 = 30 \quad \text{(True)} \]

The equations that have a solution of \( z = 3 \) are:

• \( 9z - 5 = 22 \)
• \( 54 - 8z = 30 \)

So, the two correct equations are \( 9z - 5 = 22 \) and \( 54 - 8z = 30 \).

Answer 2

(a) Mr. Gonzales has only $36 to spend at a clothing store. He wants to buy a shirt that costs $22 and some bracelets that cost $3.50 each.
Choose which equation will determine, x, the maximum number of bracelets Mr. Gonzales could buy.
x + 22 = 36
3.50x - 22 = 36
3.50x + 22 = 36
22x + 3.50 = 36

Answer 3

To determine the maximum number of bracelets Mr. Gonzales can buy, we need to set up an equation based on his total budget and the cost of the shirt and bracelets.

1. He starts with \( $36 \).
2. He wants to buy a shirt that costs \( $22 \).
3. Each bracelet costs \( $3.50 \), and we will let \( x \) be the number of bracelets he buys.

After buying the shirt, the amount he has left for bracelets is: \[ 36 - 22 = 14 \]

Now, the total cost of the bracelets he buys is \( 3.50x \). We want to find how many bracelets he can buy with the remaining \( $14 \): \[ 3.50x = 14 \]

Thus, the equation that correctly represents the situation is: \[ 3.50x + 22 = 36 \] This is because this equation represents the total expenditure being equal to his initial amount of money, with his expenditures on the shirt and bracelets accounted for.

So the correct equation to use is: \( 3.50x + 22 = 36 \).

Answer 4

(a) Mr. Gonzales has only $36 to spend at a clothing store. He wants to buy a shirt that costs $22 and some bracelets that cost $3.50 each. Choose which equation will determine, x, the maximum number of bracelets Mr. Gonzales could buy.
x + 22 = 36
3.50x - 22 = 36
3.50x + 22 = 36
22x + 3.50 = 36
​Solve the equation to determine the number of bracelets Mr. Gonzales could buy.
x=__

Answer 5

To find the maximum number of bracelets Mr. Gonzales can buy, we can use the correct equation from the options provided:

\( 3.50x + 22 = 36 \)

Now, let's solve for \( x \):

1. Subtract \( 22 \) from both sides of the equation: \[ 3.50x + 22 - 22 = 36 - 22 \] \[ 3.50x = 14 \]

2. Next, divide both sides by \( 3.50 \) to isolate \( x \): \[ x = \frac{14}{3.50} \]

3. Now calculate \( \frac{14}{3.50} \): \[ x = \frac{14}{3.50} = \frac{14}{\frac{7}{2}} = 14 \times \frac{2}{7} = \frac{28}{7} = 4 \]

Therefore, Mr. Gonzales can buy \( x = 4 \) bracelets.

Answer 6

solve the equation for x
3(2x+4)=6
x=__

Answer 7

To solve the equation \( 3(2x + 4) = 6 \) for \( x \), follow these steps:

1. Start by distributing the \( 3 \) on the left side of the equation: \[ 3 \cdot 2x + 3 \cdot 4 = 6 \] This simplifies to: \[ 6x + 12 = 6 \]

2. Next, subtract \( 12 \) from both sides of the equation to isolate the term with \( x \): \[ 6x + 12 - 12 = 6 - 12 \] This reduces to: \[ 6x = -6 \]

3. Now, divide both sides by \( 6 \) to solve for \( x \): \[ x = \frac{-6}{6} = -1 \]

Therefore, the solution is: \[ x = -1 \]

Answer 8

solve the equation for n:
7(n-3)=-21
n=__

Answer 9

To solve the equation \( 7(n - 3) = -21 \) for \( n \), follow these steps:

1. Distribute the 7 on the left side of the equation: \[ 7n - 21 = -21 \]

2. Add 21 to both sides of the equation to isolate the term with \( n \): \[ 7n - 21 + 21 = -21 + 21 \] This simplifies to: \[ 7n = 0 \]

3. Now, divide both sides by \( 7 \) to solve for \( n \): \[ n = \frac{0}{7} = 0 \]

Thus, the solution is: \[ n = 0 \]