What is the solution of the equation 10z − 6 = 24 solving for z ?(1 point)

Question

Responses

−3
negative 3

0.4
0.4

3
3

1.8
1.8

Answer 1

To solve the equation \( 10z - 6 = 24 \) for \( z \), follow these steps:

1. Add 6 to both sides of the equation:

   \[ 10z - 6 + 6 = 24 + 6 \]

   This simplifies to:

   \[ 10z = 30 \]

2. Divide both sides by 10:

   \[ z = \frac{30}{10} \]

   This simplifies to:

   \[ z = 3 \]

So, the solution is \( z = 3 \).

Answer 2

Jonny is solving this equation for n : 8 + 3n = 20 . His first step is to subtract 8 from both sides of the equation. Why?(1 point)
Responses

He needs to follow the order of operations.
He needs to follow the order of operations.

8 is attached to 3n by subtraction.
8 is attached to 3 n by subtraction.

He needs to reverse the order of operations.
He needs to reverse the order of operations.

8 is the first term in the equation.
8 is the first term in the equation.

Answer 3

The correct reasoning for Jonny subtracting 8 from both sides of the equation \( 8 + 3n = 20 \) is:

8 is attached to 3n by subtraction.

By subtracting 8, Jonny is isolating the term with \( n \) so that he can solve for \( n \) more easily. The other options do not accurately describe the reasoning behind his step.

Answer 4

Samuel is solving an equation for y . His first step is to add 7 to both sides. Which equation is he solving?(1 point)
Responses

2y + 7 = 15
2 y plus 7 equals 15

2y − 15 = 7
2 y minus 15 equals 7

2y − 7 = 15
2 y minus 7 equals 15

2y + 15 = 7

Answer 5

To determine which equation Samuel is solving when his first step is to add 7 to both sides, we need to identify an equation where 7 can be removed by adding it to both sides.

The equation that fits this scenario is:

2y - 7 = 15.

In this equation, if Samuel adds 7 to both sides, he would get:

\[ 2y - 7 + 7 = 15 + 7 \]

Which simplifies to:

\[ 2y = 22. \]

Thus, Samuel is solving the equation \( 2y - 7 = 15 \).