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Identify the first step in solving this equation for x

: −3 = x/4 + 2
.(1 point)
Responses

Divide both sides by 4.
Divide both sides by 4.

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.

9 answers

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.

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

1.8
1.8

0.4
0.4

−3
negative 3

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

So the solution for \(z\) is 3.

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

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

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

8 is the first term in the equation.

Jonny's first step is to subtract 8 from both sides of the equation \(8 + 3n = 20\) because:

8 is attached to 3n by addition.

By subtracting 8 from both sides, he isolates the term with \(n\) on one side of the equation.

However, since that exact response isn't available in your options, the closest correct reasoning to his choice is:

8 is attached to 3n by subtraction.

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 plus 15 equals 7

2y − 15 = 7
2 y minus 15 equals 7

2y − 7 = 15

Samuel's first step is to add 7 to both sides. This implies that he is likely working with an equation where 7 is subtracted from another term. Let's analyze each option:

  1. \(2y + 7 = 15\): If he adds 7 to both sides, he would move further away from isolating \(y\).

  2. \(2y + 15 = 7\): Adding 7 to both sides would increase the left side, which doesn't make sense in this context.

  3. \(2y - 15 = 7\): If he adds 7 to both sides, he would actually be preparing to isolate \(2y\) by the operation \(2y - 15 + 15 = 7 + 7\).

  4. \(2y - 7 = 15\): Here, if he adds 7 to both sides, it makes sense as it would lead to \(2y = 15 + 7\).

Among these options, the correct equation that supports his first step of adding 7 is:

\(2y - 7 = 15\).

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 + x4 = 1
6 plus Start Fraction x over 4 End Fraction equals 1

4 + x6 = 1
4 plus Start Fraction x over 6 End Fraction equals 1

4 + 6x = 1
4 plus 6 x equals 1

6 + 4x = 1

To determine which equation Kelia is solving, we need to understand that her second step involves multiplying both sides by 4. This suggests that, during her first step, she must have had a fraction that needed to be eliminated by multiplication.

Let's analyze the provided equations:

  1. \(6 + \frac{x}{4} = 1\): If her first step involved isolating \(\frac{x}{4}\) and her second step is to multiply both sides by 4, it would eliminate the fraction: \[ 4(6 + \frac{x}{4}) = 4(1) \implies 24 + x = 4. \] This would be consistent with multiplying by 4 after isolating the fraction.

  2. \(4 + \frac{x}{6} = 1\): In this case, multiplying by 4 wouldn't directly relate to \(\frac{x}{6}\).

  3. \(4 + 6x = 1\): This equation doesn't involve any fractions, so multiplying by 4 would not be a relevant step.

  4. \(6 + 4x = 1\): Similarly, this equation does not feature a fraction.

Given the calculations, the equation that makes sense for Kelia's process—having a fraction that she would multiply by 4 to eliminate—is:

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