Ask a New Question
Menu

-15x + 24 + 16x = 3x - 24

What is a step that can be used to transform the equation into the form x = a, where a is a number, to show that the equation has one solution? Select TWO options that apply.

3 answers

To transform the equation \(-15x + 24 + 16x = 3x - 24\) into the form \(x = a\) where \(a\) is a number, you can follow these steps:

  1. Combine like terms on the left side: Combine \(-15x + 16x\) to simplify the left side of the equation. This results in: \[1x + 24 = 3x - 24\]

  2. Isolate \(x\) on one side of the equation: You can do this by subtracting \(3x\) from both sides and also subtracting \(24\) from both sides. This will give you: \[1x - 3x = -24 - 24\]

    Simplifying this gives: \[-2x = -48\]

    Finally, divide both sides by \(-2\) to solve for \(x\): \[x = 24\]

So, the two applicable steps are:

  • Combine like terms on the left side of the equation.
  • Isolate \(x\) on one side of the equation.

These steps will lead you to a solution that shows the equation has one solution.

how do you isolate x

Isolating \(x\) in an equation means rearranging the equation so that \(x\) is by itself on one side of the equation, typically on the left. Let’s walk through the steps using your original equation:

Original Equation:

\[ -15x + 24 + 16x = 3x - 24 \]

Step 1: Combine Like Terms

First, combine the \(x\) terms on the left side: \[ (-15x + 16x) + 24 = 3x - 24 \] This simplifies to: \[ 1x + 24 = 3x - 24 \] Or, just: \[ x + 24 = 3x - 24 \]

Step 2: Move all \(x\) Terms to One Side

Next, to isolate \(x\), we want to get all terms involving \(x\) on one side of the equation and the constants on the other side. To do this, subtract \(3x\) from both sides: \[ x - 3x + 24 = -24 \] This simplifies to: \[ -2x + 24 = -24 \]

Step 3: Move Constant Terms to the Other Side

Now, subtract \(24\) from both sides to isolate the \(x\) term: \[ -2x = -24 - 24 \] This simplifies to: \[ -2x = -48 \]

Step 4: Solve for \(x\)

Finally, divide both sides by \(-2\) to solve for \(x\): \[ x = \frac{-48}{-2} = 24 \]

Summary

So the combination of steps to isolate \(x\) involves:

  1. Combining like terms.
  2. Moving \(x\) terms to one side (via addition or subtraction).
  3. Moving constant terms to the other side.
  4. Dividing or multiplying as necessary to solve for \(x\).

In this case, you found that: \[ x = 24 \] This means the equation has a unique solution, which is \(x = 24\).