Question

Can you please help me with Solve the inequality: −15−7x≤−11+13x Enter your answer as an interval, such as [a,∞) .

Answer 1

We have the following inequaltiy:

$-15-7x\le-11+13x$

By adding 11 to both sides, we have

$-4-7x\le13x$

Now, by adding 7x to both sides, we obtain

$-4\le20x$

or equivalently,

$20x\ge-4$

Finally, by dividing both sides by 20, we have

$\begin{gathered} x\ge\frac{-4}{20} \\ \text{then} \\ x\ge-\frac{1}{5} \end{gathered}$

Therefore, the answer in interval notation is:

$\lbrack-\frac{1}{5},\infty)$