Question

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

Answer 1

Given:

`6x\text{ + }(1)/(4)(4x\text{ + 8) > 12}`

First, let's open the bracket:

`\begin{gathered} 6x\text{ + }(1)/(4)*\text{ 4x + }(1)/(4)*8\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} (7x)/(7)\text{ > }(10)/(7) \\ x\text{ > }(10)/(7) \end{gathered}`

Solution:

x > 10/7