Solve the inequality and specify any excluded values? $- 2 < \frac{3 x + 1}{x - 3}$ $-2 < (3x+1)/(x-3)$

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Answer 1 · 2017-02-28T19:03:57

$x > 1, x \neq 3$ $x>1, x!=3$

First, keep in mind that you need

$x - 3 \neq 0 \Rightarrow x \neq 3$ $x - 3 !=0 implies x !=3$

since $x = 3$ $x=3$ would make the denominator equal to $0$ $0$ .

Now, multiply both sides by $x - 3$ $x-3$ to get

$- 2 (x - 3) < 3 x + 1$ $-2(x-3) < 3x+1$

Next, expand the brackets

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

Don't forget your rules for multiplying negatives!

Next, do some rearranging to get the $x$ $x$ 's on one side and the other terms on the other side

$6 < 5 x + 1$ $6 < 5x+1$

$5 < 5 x$ $5 < 5x$

Therefore,

$1 < x$ $1 < x " "$ or $x > 1$ $" "x > 1$

I hope this helps.

Solve the inequality and specify any excluded values? -2 < (3x+1)/(x-3)−2<3x+1x−3-2 < (3x+1)/(x-3)