Question

Solve and graph the solution: $-^\frac{1}{5} \leq^\frac{3x}{10}+1\ \textless \ 1^\frac{1}{5}x \hspace{3} R.$

Answer 1

Answer:

[-4, 2/3)

Step-by-step explanation:

The solution of this inequality is obtained by simplification.

$\frac{-1}{5}\leq\frac{3x}{10}+1\leq1\frac{1}{5}\\\\\frac{-1}{5}\leq\frac{3x}{10}+1\leq\frac{6}{5}$

subtract throughout by 1

$\frac{-1}{5}-1\leq\frac{3x}{10}+1-1\leq\frac{6}{5}-1\\\\\frac{-6}{5}\leq\frac{3x}{10}\leq\frac{1}{5}$

Multiply throughout by 10

$\frac{-6}{5}(10)\leq\frac{3x}{10}(10)\leq\frac{1}{5}(10)\\\\-12\leq3x\leq2$

Divide throughout by 3

$-4\leq x\leq\frac{2}{3}$

⇒ x∈ [-4, 2/3)

I hope this answer helps you.