# How do you solve 4(x – 3) + 4 <10 + 6x?

Jun 20, 2017

$x > 9$

#### Explanation:

Expand the bracket on the LHS by multiplying $x$ with $4$ and $- 3$ with $4$.

$4 x - 12 + 4 < 10 + 6 x$

$4 x - 8 < 10 + 6 x$

$4 x < 18 + 6 x$

$- 2 x < 18$

Now, divide the entire equation by $- 2$. But keep in mind the the equality sign FLIPS when you divide by a negative number.

$x > 9$

Below is the graph of this inequalities.

graph{x>9 [-0.76, 72.3, 0.74, 37.27]}

Jun 20, 2017

See a solution process below:

#### Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{4} \left(x - 3\right) + 4 < 10 + 6 x$

$\left(\textcolor{red}{4} \cdot x\right) - \left(\textcolor{red}{4} \cdot 3\right) + 4 < 10 + 6 x$

$4 x - 12 + 4 < 10 + 6 x$

$4 x - 8 < 10 + 6 x$

Next, subtract $\textcolor{red}{4 x}$ and $\textcolor{b l u e}{10}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$4 x - 8 - \textcolor{red}{4 x} - \textcolor{b l u e}{10} < 10 + 6 x - \textcolor{red}{4 x} - \textcolor{b l u e}{10}$

$4 x - \textcolor{red}{4 x} - 8 - \textcolor{b l u e}{10} < 10 - \textcolor{b l u e}{10} + 6 x - \textcolor{red}{4 x}$

$0 - 18 < 0 + \left(6 - \textcolor{red}{4}\right) x$

$- 18 < 2 x$

Now, divide each side of the inequality by $\textcolor{red}{2}$ to solve for $x$ while keeping the equation balanced:

$- \frac{18}{\textcolor{red}{2}} < \frac{2 x}{\textcolor{red}{2}}$

$- 9 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}}$

$- 9 < x$

To state the solution in terms of $x$ we can reverse or "flip" the entire inequality:

$x > - 9$