# How do you solve and write the following in interval notation: 2x − 1 < x + 6 <3x − 4 ?

##### 1 Answer
Oct 27, 2017

$7 > x > 5$

#### Explanation:

$2 x - 1 < x + 6 < 3 x - 4$

We will divide the equations into two parts!

$2 x - 1 < x + 6 \mathmr{and} x + 6 < 3 x - 4$

Solving the First Part!

$2 x - 1 < x + 6$

Subtract $x$ from both sides..

$2 x - 1 - x < x + 6 - x$

$2 x - x - 1 < x - x + 6$

$x - 1 < 0 + 6$

$x - 1 < 6$

Add $1$ to both sides

$x - 1 + 1 < 6 + 1$

$x + 0 < 7$

$x < 7$

Same as $7 > x$

Solving the Second Part!

$x + 6 < 3 x - 4$

Subtract $x$ from both sides..

$x + 6 - x < 3 x - 4 - x$

$x - x + 6 < 3 x - x - 4$

$0 + 6 < 2 x - 4$

$6 < 2 x - 4$

Add $4$ to both sides..

$6 + 4 < 2 x - 4 + 4$

$10 < 2 x + 0$

$10 < 2 x$

Divide both sides by $2$

$\frac{10}{2} < \frac{2 x}{2}$

$\frac{10}{2} < \frac{\cancel{2} x}{\cancel{2}}$

$\frac{10}{2} < x$

$5 < x$

Same as $x > 5$

Hence adding both..

$7 > x > 5$