Graph 2x-3<=4x+3<2x+5

$2 x - 3 \leq 4 x + 3 < 2 x + 5$

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

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

$2 x - 3 - 3 \leq 4 x < 2 x + 5 - 3$

Subtract $3$ from $- 3$ .

$2 x - 6 \leq 4 x < 2 x + 5 - 3$

Subtract $3$ from $5$ .

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

Divide each term in the inequality by $4$ .

$\frac{2 x}{4} + \frac{- 6}{4} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

Simplify each term.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{4} + \frac{- 6}{4} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 x}{2 \cdot 2} + \frac{- 6}{4} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

Cancel the common factor.

$\frac{2 x}{2 \cdot 2} + \frac{- 6}{4} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

Rewrite the expression.

$\frac{x}{2} + \frac{- 6}{4} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

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

Factor $2$ out of $- 6$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{2} + \frac{- 3}{2} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

Move the negative in front of the fraction.

$\frac{x}{2} - \frac{3}{2} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x}{2} - \frac{3}{2} \leq \frac{4 x}{4} < \frac{2 x}{4} + \frac{2}{4}$

Divide $x$ by $1$ .

$\frac{x}{2} - \frac{3}{2} \leq x < \frac{2 x}{4} + \frac{2}{4}$

Simplify each term.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{2} - \frac{3}{2} \leq x < \frac{x}{2} + \frac{2}{4}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$\frac{x}{2} - \frac{3}{2} \leq x < \frac{x}{2} + \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{x}{2} - \frac{3}{2} \leq x < \frac{x}{2} + \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$\frac{x}{2} - \frac{3}{2} \leq x < \frac{x}{2} + \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$\frac{x}{2} - \frac{3}{2} \leq x < \frac{x}{2} + \frac{1}{2}$

Graph 2x-3<=4x+3<2x+5

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