Graph 7/3-1/2x>=7/6+x

$\frac{7}{3} - \frac{1}{2} x \geq \frac{7}{6} + x$

Step 1

Combine $x$ and $\frac{1}{2}$ .

$\frac{7}{3} - \frac{x}{2} \geq \frac{7}{6} + x$

Step 2

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

Subtract $x$ from both sides of the inequality.

$\frac{7}{3} - \frac{x}{2} - x \geq \frac{7}{6}$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7}{3} - \frac{x}{2} - x \cdot \frac{2}{2} \geq \frac{7}{6}$

Combine $- x$ and $\frac{2}{2}$ .

$\frac{7}{3} - \frac{x}{2} + \frac{- x \cdot 2}{2} \geq \frac{7}{6}$

Combine the numerators over the common denominator.

$\frac{7}{3} + \frac{- x - x \cdot 2}{2} \geq \frac{7}{6}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x - x \cdot 2$ .

Factor $x$ out of $- x$ .

$\frac{7}{3} + \frac{x \cdot - 1 - x \cdot 2}{2} \geq \frac{7}{6}$

Factor $x$ out of $- x \cdot 2$ .

$\frac{7}{3} + \frac{x \cdot - 1 + x (- 1 \cdot 2)}{2} \geq \frac{7}{6}$

Factor $x$ out of $x \cdot - 1 + x (- 1 \cdot 2)$ .

$\frac{7}{3} + \frac{x (- 1 - 1 \cdot 2)}{2} \geq \frac{7}{6}$

Multiply $- 1$ by $2$ .

$\frac{7}{3} + \frac{x (- 1 - 2)}{2} \geq \frac{7}{6}$

Subtract $2$ from $- 1$ .

$\frac{7}{3} + \frac{x \cdot - 3}{2} \geq \frac{7}{6}$

Move $- 3$ to the left of $x$ .

$\frac{7}{3} + \frac{- 3 \cdot x}{2} \geq \frac{7}{6}$

Move the negative in front of the fraction.

$\frac{7}{3} - \frac{3 x}{2} \geq \frac{7}{6}$

Step 3

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

Subtract $\frac{7}{3}$ from both sides of the inequality.

$- \frac{3 x}{2} \geq \frac{7}{6} - \frac{7}{3}$

To write $- \frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 x}{2} \geq \frac{7}{6} - \frac{7}{3} \cdot \frac{2}{2}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{3}$ by $\frac{2}{2}$ .

$- \frac{3 x}{2} \geq \frac{7}{6} - \frac{7 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$- \frac{3 x}{2} \geq \frac{7}{6} - \frac{7 \cdot 2}{6}$

Combine the numerators over the common denominator.

$- \frac{3 x}{2} \geq \frac{7 - 7 \cdot 2}{6}$

Simplify the numerator.

Multiply $- 7$ by $2$ .

$- \frac{3 x}{2} \geq \frac{7 - 14}{6}$

Subtract $14$ from $7$ .

$- \frac{3 x}{2} \geq \frac{- 7}{6}$

Move the negative in front of the fraction.

$- \frac{3 x}{2} \geq - \frac{7}{6}$

Step 4

Divide each term in $- \frac{3 x}{2} \geq - \frac{7}{6}$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{2} \geq - \frac{7}{6}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{2}}{- 1} \leq \frac{- \frac{7}{6}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{2}}{1} \leq \frac{- \frac{7}{6}}{- 1}$

Divide $\frac{3 x}{2}$ by $1$ .

$\frac{3 x}{2} \leq \frac{- \frac{7}{6}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$\frac{3 x}{2} \leq \frac{\frac{7}{6}}{1}$

Divide $\frac{7}{6}$ by $1$ .

$\frac{3 x}{2} \leq \frac{7}{6}$

Step 5

Multiply both sides by $2$ .

$\frac{3 x}{2} \cdot 2 \leq \frac{7}{6} \cdot 2$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x}{2} \cdot 2 \leq \frac{7}{6} \cdot 2$

Rewrite the expression.

$3 x \leq \frac{7}{6} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$3 x \leq \frac{7}{2 (3)} \cdot 2$

Cancel the common factor.

$3 x \leq \frac{7}{2 \cdot 3} \cdot 2$

Rewrite the expression.

$3 x \leq \frac{7}{3}$

Step 7

Divide each term in $3 x \leq \frac{7}{3}$ by $3$ and simplify.

Divide each term in $3 x \leq \frac{7}{3}$ by $3$ .

$\frac{3 x}{3} \leq \frac{\frac{7}{3}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{\frac{7}{3}}{3}$

Divide $x$ by $1$ .

$x \leq \frac{\frac{7}{3}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x \leq \frac{7}{3} \cdot \frac{1}{3}$

Multiply $\frac{7}{3} \cdot \frac{1}{3}$ .

Multiply $\frac{7}{3}$ by $\frac{1}{3}$ .

$x \leq \frac{7}{3 \cdot 3}$

Multiply $3$ by $3$ .

$x \leq \frac{7}{9}$

Step 8

Graph 7/3-1/2x>=7/6+x

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