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

Question

-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.

GPT-4o mini · Answer

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.

T-Swizzle · Answer

how do you isolate x

GPT-4o mini · Answer

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:

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

Step 1: Combine Like Terms

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

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 $3 x$ from both sides: $x - 3 x + 24 = - 24$ This simplifies to: $- 2 x + 24 = - 24$

Step 3: Move Constant Terms to the Other Side

Now, subtract $24$ from both sides to isolate the $x$ term: $- 2 x = - 24 - 24$ This simplifies to: $- 2 x = - 48$

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:

Combining like terms.
Moving $x$ terms to one side (via addition or subtraction).
Moving constant terms to the other side.
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 $x = 24$ .