Can you check the following problem? (forgot to incl last night)

1. Which is an equivalent equation to (2/3)x - 1 = 1/2 that does not contain fractions?

(2/3)x = 1 + 1/2
(2/3)x = 3/2
x = 3/2 * 3/2
x = 9/4
x = 2 1/4

A. 4x - 6 = 3
4x = 9
x = 9/4
x = 2 1/4

B. 4x - 2 = 3
4x = 5
x = 5/4
x = 1 1/4

C. 3x - 2 = 1
3x = 3
x = 1

D. 2x - 3 = 3/2
2x = 3/2 + 3
2x = 3/2 + 6/2
2x = 9/2
x = 9/4
x = 2 1/4

ANs: I'm not sure. Choice C is the only that doesn't include a fraction. But, it doesn't make the original equation true. Choice A and D both have same answer as original equation. Can you explain how to do this?

It says to find the equivalent equation containing no fractions.

It did not ask to find the solution, so

(2/3)x - 1 = 1/2
multiply each term by 6 , the LCD
6(2/3)x - 6(1) = 6(1/2)
4x - 6 = 3

which is choice A

Oh.thank you!

2/3x + 1 = 1/2

To find an equivalent equation to (2/3)x - 1 = 1/2 that does not contain fractions, we need to get rid of the fractions by using the properties of equality. Here's how you can solve this problem step by step:

Step 1: Get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD) to clear the fractions. In this case, the LCD is 6, because it is the least common multiple of 3 and 2.

6 * ((2/3)x - 1) = 6 * (1/2)

Simplifying both sides of the equation gives us:

4x - 6 = 3

Step 2: Now we have the equivalent equation 4x - 6 = 3, which does not contain fractions.

Let's check the answer choices:

A. 4x - 6 = 3

If we solve this equation, we get:

4x = 9
x = 9/4
x = 2 1/4

So, choice A is indeed an equivalent equation to the original equation that does not contain fractions.

B. 4x - 2 = 3

If we solve this equation, we get:

4x = 5
x = 5/4
x = 1 1/4

This is not the correct answer since it does not match the equivalent value we found earlier.

C. 3x - 2 = 1

If we solve this equation, we get:

3x = 3
x = 1

This equation does not satisfy the original equation, so it is not correct.

D. 2x - 3 = 3/2

If we solve this equation, we get:

2x = 3/2 + 3
2x = 3/2 + 6/2
2x = 9/2
x = 9/4
x = 2 1/4

This is the same as our earlier calculation and is also an equivalent equation to the original equation.

So, both choices A and D are correct.