How do you solve 3x-5>15-2x?

May 15, 2015

You can always add (or subtract) the same amount to both sides of an inequality without effecting the orientation of the inequality.

You can always multiply or divide both sides of an inequality by the same amount provided that amount is greater than zero without effecting the orientation of the inequality.

Given $3 x - 5 > 15 - 2 x$

We can add $2 x + 5$ to both sides:
$5 x > 20$

then divide both sides by $5$
$x > 4$

May 15, 2015

The answer is $x > 4$ or x in (4;+oo)

To solve the inequality you have to "move" $- 2 x$ to the left side and $- 5$ to the right.
$3 x + 2 x > 15 + 5$
$5 x > 20$
Now after dividing by $4$ you get the solution
$x > 4$

May 15, 2015

The answer is $x > 4$.

Solve $3 x - 5 > 15 - 2 x$.

Add $2 x$ to both sides of the inequality.

$2 x + 3 x - 5 > 15 - 2 x + 2 x$ =

$5 x - 5 > 15$

Add $5$ to both sides.

$5 + 5 x - 5 > 15 + 5$ =

$5 x > 20$

Divide both sides by $5$.

$\frac{{\cancel{5}}^{1} x}{\cancel{{5}^{1}}} > {\cancel{20}}^{4} / {\cancel{5}}^{1}$ =

$x > 4$