Question

Solve 4/7x−2/7>5/7 . Write the rational number in your answer as a mixed number. Make sure to write your inequality so that x comes first.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will isolate x.

First, let's add 2/7 to both sides of the inequality:
4/7x - 2/7 + 2/7 > 5/7 + 2/7
This simplifies to:
4/7x > 7/7

Next, let's simplify 7/7:
4/7x > 1

To isolate x, we'll divide both sides of the inequality by 4/7. Remember, when dividing by a fraction, you need to multiply by the reciprocal:
(4/7x)/(4/7) > (1)/(4/7)
This simplifies to:
x > (1)/(4/7)

To divide by 4/7, we can multiply by its reciprocal, which is 7/4:
x > (1)/(4/7) * (7/4)
This simplifies to:
x > (7)/(4/7)

To multiply fractions, we can multiply the numerators and denominators separately:
x > 7/1 * 7/4

Multiplying the numerators gives us:
x > 49/4

Therefore, the solution to the inequality is x > 49/4. Written as a mixed number, this is:
x > 12 1/4

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake. Let's solve the inequality correctly:

First, let's simplify both sides of the inequality:
4/7x - 2/7 > 5/7

To do this, we need to find a common denominator for all the fractions involved, which in this case is 7.

Now, we'll apply the common denominator to all the fractions:
(4/7)x - (2/7) > (5/7)

Next, let's simplify the equation:
(4x - 2)/7 > 5/7

To eliminate the denominator, we can multiply both sides of the inequality by 7:
7 * ((4x - 2)/7) > 7 * (5/7)

Simplifying both sides gives us:
4x - 2 > 5

Now, let's isolate x. We'll first add 2 to both sides of the inequality:
4x - 2 + 2 > 5 + 2
4x > 7

Finally, to solve for x, divide both sides of the inequality by 4:
(4x)/4 > 7/4
x > 7/4

Therefore, the solution to the inequality is x > 7/4. We can also write it as a mixed number:
x > 1 3/4