Question

look at the equation below -10x+13+12x=5x-8 which of the following steps would be used to transform the equation into the form x=a where a is the number to show that the equation has one solution select two options that apply

Answer 1

To solve the equation -10x + 13 + 12x = 5x - 8 and transform it into the form x = a, we can follow these steps:

1. **Combine like terms:** On the left side, we can combine -10x and 12x.
- This gives us: \( (-10x + 12x) + 13 = 5x - 8 \)
- Resulting in: \( 2x + 13 = 5x - 8 \)

2. **Isolate the variable x:** To isolate x, we need to move the terms involving x to one side and constant terms to the other side. We can do this by subtracting 2x from both sides.
- This gives us: \( 13 = 5x - 2x - 8 \)
- Resulting in: \( 13 = 3x - 8 \)

3. **Add or subtract constants to isolate x:** Next, we would add 8 to both sides to isolate the term involving x.
- This gives us: \( 13 + 8 = 3x \)
- Resulting in: \( 21 = 3x \)

4. **Divide by the coefficient of x:** Finally, we would divide both sides by 3 to solve for x.
- Resulting in: \( x = 7 \)

Therefore, the two applicable steps that would be used to transform the equation into the form x = a are:

1. Combine like terms.
2. Isolate the variable x (which may involve adding, subtracting, etc.).

Using these strategies in the appropriate order helps show that the equation has one solution.