Solve the Inequality for x 4x-3<-1x+12

$4 x - 3 < - 1 x + 12$

Step 1

Rewrite $- 1 x$ as $- x$ .

$4 x - 3 < - x + 12$

Step 2

Move all terms containing $x$ to the left side of the inequality.

Add $x$ to both sides of the inequality.

$4 x - 3 + x < 12$

Add $4 x$ and $x$ .

$5 x - 3 < 12$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$5 x < 12 + 3$

Add $12$ and $3$ .

$5 x < 15$

Step 4

Divide each term in $5 x < 15$ by $5$ and simplify.

Divide each term in $5 x < 15$ by $5$ .

$\frac{5 x}{5} < \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} < \frac{15}{5}$

Divide $x$ by $1$ .

$x < \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x < 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 3$

Interval Notation:

$(- \infty, 3)$