# How do solve #1/4<7/(7-x)# algebraically?

The steps to solving any nonlinear inequality are:

The solution will be those intervals in which the function has the correct signs satisfying the inequality.

We can rearrange the equation as follows:

Which we can write as:

So, the critical points where a sign change can occur, are:

{: ( ul("factor"), ul(x lt -21), ul(-21 lt x lt 7), ul(x gt 7) ), ( x+21, -, +, + ), ( x-7, -, -, + ), ( { x + 21 } / { x-7 }, +,- ,+ ) :}

By signing up, you agree to our Terms of Service and Privacy Policy

To solve the inequality (\frac{1}{4} < \frac{7}{7 - x}) algebraically:

- Multiply both sides of the inequality by (4) to clear the fraction:

[4 \times \frac{1}{4} < 4 \times \frac{7}{7 - x}]

[1 < \frac{28}{7 - x}]

- Cross-multiply to eliminate the fraction:

[1(7 - x) < 28]

[7 - x < 28]

- Subtract (7) from both sides of the inequality:

[7 - x - 7 < 28 - 7]

[ - x < 21]

- Divide both sides of the inequality by (-1), remember to flip the inequality sign:

[x > -21]

So, the solution to the inequality is (x > -21).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7