Identify the first step in solving this equation for x: −3 = x4 + 2.

Question

Multiply both sides by 2.
Add 2 to both sides.
Divide both sides by 4.
Subtract 2 from both sides.

Answer 1

The first step in solving the equation \(-3 = x^4 + 2\) for \(x\) is to subtract 2 from both sides. This isolates the term involving \(x\).

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

Answer 2

What is the solution of the equation 10z − 6 = 24 solving for z ?

Answer 3

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

1. Add 6 to both sides of the equation to eliminate the \(-6\): \[ 10z - 6 + 6 = 24 + 6 \] This simplifies to: \[ 10z = 30 \]

2. Divide both sides by 10 to solve for \(z\): \[ z = \frac{30}{10} \] This simplifies to: \[ z = 3 \]

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

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?
He needs to follow the order of operations.
8 is the first term in the equation.
8 is attached to 3n by subtraction.
He needs to reverse the order of operations.

Answer 5

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

This means that to isolate the term \(3n\), he needs to eliminate the \(8\) on the left side of the equation. Therefore, the correct answer is:

8 is attached to 3n by subtraction.

Answer 6

are you sure it isn't D.He needs to reverse the order of operation

Answer 7

Let's clarify the situation regarding why Jonny would subtract 8 from both sides of the equation \(8 + 3n = 20\).

When solving an equation, the goal is to isolate the variable. In this case, Jonny wants to isolate \(3n\). Since \(8\) is added to \(3n\), the first step to isolate \(3n\) is to subtract \(8\) from both sides. This is a fundamental principle of algebra, and it doesn’t involve reversing the order of operations in the traditional sense.

The term "order of operations" usually refers to the rules (PEMDAS/BODMAS) used to evaluate expressions (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In the context of solving an equation, we are applying inverse operations to isolate variables, not reversing the order of operations. Therefore, the best answer in this context remains:

8 is attached to 3n by subtraction.

So the reasoning does not correctly fit the statement in option D, "He needs to reverse the order of operations." Therefore, the original reasoning stands reaffirmed.

Answer 8

Samuel is solving an equation for y . His first step is to add 7 to both sides. Which equation is he solving?
2y + 15 = 7
2y − 15 = 7
2y − 7 = 15
2y + 7 = 15

Answer 9

To determine which equation Samuel is solving when he adds \(7\) to both sides, we can evaluate each option by considering what happens if we add \(7\) to both sides of the equation.

1. For the equation \(2y + 15 = 7\):

   • Adding \(7\) to both sides: \[ 2y + 15 + 7 = 7 + 7 \quad \Rightarrow \quad 2y + 22 = 14 \] (This does not directly isolate \(y\) in a clear manner with the addition of 7.)

2. For the equation \(2y - 15 = 7\):

   • Adding \(7\) to both sides: \[ 2y - 15 + 7 = 7 + 7 \quad \Rightarrow \quad 2y - 8 = 14 \] (This also does not isolate \(y\).)

3. For the equation \(2y - 7 = 15\):

   • Adding \(7\) to both sides: \[ 2y - 7 + 7 = 15 + 7 \quad \Rightarrow \quad 2y = 22 \] (This is a valid step to isolate \(y\).)

4. For the equation \(2y + 7 = 15\):

   • Adding \(7\) to both sides: \[ 2y + 7 + 7 = 15 + 7 \quad \Rightarrow \quad 2y + 14 = 22 \] (This does not isolate \(y\) properly.)

Based on the evaluation, Samuel is likely solving the equation:

\(2y - 7 = 15\)

This is because adding \(7\) to both sides effectively aids in isolating the variable \(y\).