Identify the first step in solving this equation for x : −3 = x/4 + 2 .(1 point)

Question

Responses

Subtract 2 from both sides.
Subtract 2 from both sides.

Multiply both sides by 2.
Multiply both sides by 2.

Add 2 to both sides.
Add 2 to both sides.

Divide both sides by 4.

Answer 1

The first step in solving the equation \( -3 = \frac{x}{4} + 2 \) for \( x \) is to subtract 2 from both sides.

So, the correct response is: Subtract 2 from both sides.

Answer 2

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

−3
negative 3

3
3

0.4
0.4

1.8

Answer 3

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

1. Add 6 to both sides:

   \[ 10z - 6 + 6 = 24 + 6 \] \[ 10z = 30 \]

2. Divide both sides by 10:

   \[ z = \frac{30}{10} = 3 \]

Therefore, the solution for \( z \) is \( 3 \).

The correct response is: 3.

Answer 4

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.

Answer 5

Jonny subtracts 8 from both sides of the equation \( 8 + 3n = 20 \) to isolate the term with \( n \). This is because he wants to simplify the equation by getting rid of the constant on the left side.

The correct response is: 8 is attached to 3n by subtraction.

Answer 6

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 minus 7 equals 15

2y − 15 = 7
2 y minus 15 equals 7

2y + 7 = 15
2 y plus 7 equals 15

2y + 15 = 7

Answer 7

If Samuel's first step is to add 7 to both sides of the equation, he is likely solving an equation where subtracting 7 from one side gives you a value.

Let's analyze the answer choices:

1. \( 2y - 7 = 15 \)

   To isolate \( y \), you would add 7 to both sides:

   \[ 2y - 7 + 7 = 15 + 7 \implies 2y = 22 \]

2. \( 2y - 15 = 7 \)

   To isolate \( y \), you would add 15 to both sides:

   \[ 2y - 15 + 15 = 7 + 15 \implies 2y = 22 \]

3. \( 2y + 7 = 15 \)

   To isolate \( y \), you would subtract 7 from both sides, not add:

   \[ 2y + 7 - 7 = 15 - 7 \implies 2y = 8 \]

4. \( 2y + 15 = 7 \)

   To isolate \( y \), you would subtract 15 from both sides:

   \[ 2y + 15 - 15 = 7 - 15 \implies 2y = -8 \]

The only equation for which the first step makes sense—adding 7 to both sides—is:

\( 2y - 7 = 15 \)

Answer 8

Kelia is solving an equation for x. Her second step is to multiply both sides of the equation by 4. Which equation is she solving?(1 point)
Responses

6 + 4x = 1
6 plus 4 x equals 1

6 + x/4 = 1
6 plus Start Fraction x over 4 End Fraction equals 1

4 + x/6 = 1
4 plus Start Fraction x over 6 End Fraction equals 1

4 + 6x = 1

Answer 9

If Kelia's second step is to multiply both sides of an equation by 4, it suggests that in the first step she had an equation where a term involving \( x \) was divided by 4. This would imply that in the first step, she would have needed to eliminate a fraction by multiplying both sides by 4.

Let's analyze each option:

1. \( 6 + 4x = 1 \)

   In the first step, there is no division by 4. Thus, multiplying both sides by 4 wouldn't make sense as a second step.

2. \( 6 + \frac{x}{4} = 1 \)

   In this case, if her first step was to subtract 6 from both sides, the equation would look like:

   \[ \frac{x}{4} = 1 - 6 \implies \frac{x}{4} = -5 \]

   Then, multiplying both sides by 4 would lead to:

   \[ x = -20 \]

   This means this equation fits what Kelia is doing.

3. \( 4 + \frac{x}{6} = 1 \)

   Similar to before, she would need to multiply by 6, not 4, to eliminate the fraction.

4. \( 4 + 6x = 1 \)

   Again, the first step does not involve a division by 4, so this would not make sense for a second step of multiplying by 4.

From this analysis, the correct equation Kelia is solving, where her second step involves multiplying by 4, is:

\( 6 + \frac{x}{4} = 1 \).