Solve for x 3<=4x-3<19

$3 \leq 4 x - 3 < 19$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$3 + 3 \leq 4 x < 19 + 3$

Add $3$ and $3$ .

$6 \leq 4 x < 19 + 3$

Add $19$ and $3$ .

$6 \leq 4 x < 22$

Step 2

Divide each term in the inequality by $4$ .

$\frac{6}{4} \leq \frac{4 x}{4} < \frac{22}{4}$

Step 3

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$\frac{2 (3)}{4} \leq \frac{4 x}{4} < \frac{22}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 3}{2 \cdot 2} \leq \frac{4 x}{4} < \frac{22}{4}$

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 2} \leq \frac{4 x}{4} < \frac{22}{4}$

Rewrite the expression.

$\frac{3}{2} \leq \frac{4 x}{4} < \frac{22}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3}{2} \leq \frac{4 x}{4} < \frac{22}{4}$

Divide $x$ by $1$ .

$\frac{3}{2} \leq x < \frac{22}{4}$

Step 5

Cancel the common factor of $22$ and $4$ .

Factor $2$ out of $22$ .

$\frac{3}{2} \leq x < \frac{2 (11)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{3}{2} \leq x < \frac{2 \cdot 11}{2 \cdot 2}$

Cancel the common factor.

$\frac{3}{2} \leq x < \frac{2 \cdot 11}{2 \cdot 2}$

Rewrite the expression.

$\frac{3}{2} \leq x < \frac{11}{2}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$\frac{3}{2} \leq x < \frac{11}{2}$

Interval Notation:

$[\frac{3}{2}, \frac{11}{2})$

Step 7

Solve for x 3<=4x-3<19

Related Questions

Support LCMGCF.com by disabling your adblocker.