Explained: "For exercise, solve the equations and inequalities. Write..."

waigaK

Answered question

2021-10-12

For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible.

\frac{3 - x}{x + 5} \geq 1

doplovif

Skilled2021-10-13Added 71 answers

Step 1
The given inequality is

\frac{3 - x}{x + 5} \geq 1

Step 2
Solution:
We can also rewrite as

3 - x \geq x + 5

Substract 5 on both sides, we have

3 - x - 5 \geq x + 5 - 5

- 2 - x \geq x

Add x on both sides, we have

- 2 - x + x \geq x + x

- 2 \geq 2 x

Now divide each term by 2

\frac{- 2}{2} \geq \frac{2 x}{2}

\frac{- 2}{2} \geq x

- 1 \geq x

i.e.

x \leq - 1

Therefore, the interval notation for x is

[- 1, \infty)

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