Question

How do I solve one-variable inequalities with fractions and parentheses?

Answer 1

Given:

$6x\text{ + }\frac{1}{4}(4x\text{ + 8) > 12}$

First, let's open the bracket:

$\begin{gathered} 6x\text{ + }\frac{1}{4}\times\text{ 4x + }\frac{1}{4}\times8\text{ > 12} \\ 6x\text{ + x + 2 > 12} \end{gathered}$

Collect like terms:

$\begin{gathered} 6x+x\text{ > 12 - 2} \\ 7x\text{ > 10} \end{gathered}$

Divide both sides by 7:

$\begin{gathered} \frac{7x}{7}\text{ > }\frac{10}{7} \\ x\text{ > }\frac{10}{7} \end{gathered}$

Solution:

x > 10/7