Solve for x (3-4x)/6-(2x-3)/8>=2-x

$\frac{3 - 4 x}{6} - \frac{2 x - 3}{8} \geq 2 - x$

Step 1

Simplify $\frac{3 - 4 x}{6} - \frac{2 x - 3}{8}$ .

To write $\frac{3 - 4 x}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 - 4 x}{6} \cdot \frac{4}{4} - \frac{2 x - 3}{8} \geq 2 - x$

To write $- \frac{2 x - 3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 - 4 x}{6} \cdot \frac{4}{4} - \frac{2 x - 3}{8} \cdot \frac{3}{3} \geq 2 - x$

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 - 4 x}{6}$ by $\frac{4}{4}$ .

$\frac{(3 - 4 x) \cdot 4}{6 \cdot 4} - \frac{2 x - 3}{8} \cdot \frac{3}{3} \geq 2 - x$

Multiply $6$ by $4$ .

$\frac{(3 - 4 x) \cdot 4}{24} - \frac{2 x - 3}{8} \cdot \frac{3}{3} \geq 2 - x$

Multiply $\frac{2 x - 3}{8}$ by $\frac{3}{3}$ .

$\frac{(3 - 4 x) \cdot 4}{24} - \frac{(2 x - 3) \cdot 3}{8 \cdot 3} \geq 2 - x$

Multiply $8$ by $3$ .

$\frac{(3 - 4 x) \cdot 4}{24} - \frac{(2 x - 3) \cdot 3}{24} \geq 2 - x$

Combine the numerators over the common denominator.

$\frac{(3 - 4 x) \cdot 4 - (2 x - 3) \cdot 3}{24} \geq 2 - x$

Simplify the numerator.

Apply the distributive property.

$\frac{3 \cdot 4 - 4 x \cdot 4 - (2 x - 3) \cdot 3}{24} \geq 2 - x$

Multiply $3$ by $4$ .

$\frac{12 - 4 x \cdot 4 - (2 x - 3) \cdot 3}{24} \geq 2 - x$

Multiply $4$ by $- 4$ .

$\frac{12 - 16 x - (2 x - 3) \cdot 3}{24} \geq 2 - x$

Apply the distributive property.

$\frac{12 - 16 x + (- (2 x) - - 3) \cdot 3}{24} \geq 2 - x$

Multiply $2$ by $- 1$ .

$\frac{12 - 16 x + (- 2 x - - 3) \cdot 3}{24} \geq 2 - x$

Multiply $- 1$ by $- 3$ .

$\frac{12 - 16 x + (- 2 x + 3) \cdot 3}{24} \geq 2 - x$

Apply the distributive property.

$\frac{12 - 16 x - 2 x \cdot 3 + 3 \cdot 3}{24} \geq 2 - x$

Multiply $3$ by $- 2$ .

$\frac{12 - 16 x - 6 x + 3 \cdot 3}{24} \geq 2 - x$

Multiply $3$ by $3$ .

$\frac{12 - 16 x - 6 x + 9}{24} \geq 2 - x$

Add $12$ and $9$ .

$\frac{- 16 x - 6 x + 21}{24} \geq 2 - x$

Subtract $6 x$ from $- 16 x$ .

$\frac{- 22 x + 21}{24} \geq 2 - x$

Simplify with factoring out.

Factor $- 1$ out of $- 22 x$ .

$\frac{- (22 x) + 21}{24} \geq 2 - x$

Rewrite $21$ as $- 1 (- 21)$ .

$\frac{- (22 x) - 1 (- 21)}{24} \geq 2 - x$

Factor $- 1$ out of $- (22 x) - 1 (- 21)$ .

$\frac{- (22 x - 21)}{24} \geq 2 - x$

Simplify the expression.

Rewrite $- (22 x - 21)$ as $- 1 (22 x - 21)$ .

$\frac{- 1 (22 x - 21)}{24} \geq 2 - x$

Move the negative in front of the fraction.

$- \frac{22 x - 21}{24} \geq 2 - x$

Step 2

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

Add $x$ to both sides of the inequality.

$- \frac{22 x - 21}{24} + x \geq 2$

To write $x$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$- \frac{22 x - 21}{24} + x \cdot \frac{24}{24} \geq 2$

Combine $x$ and $\frac{24}{24}$ .

$- \frac{22 x - 21}{24} + \frac{x \cdot 24}{24} \geq 2$

Combine the numerators over the common denominator.

$\frac{- (22 x - 21) + x \cdot 24}{24} \geq 2$

Simplify the numerator.

Apply the distributive property.

$\frac{- (22 x) - - 21 + x \cdot 24}{24} \geq 2$

Multiply $22$ by $- 1$ .

$\frac{- 22 x - - 21 + x \cdot 24}{24} \geq 2$

Multiply $- 1$ by $- 21$ .

$\frac{- 22 x + 21 + x \cdot 24}{24} \geq 2$

Move $24$ to the left of $x$ .

$\frac{- 22 x + 21 + 24 \cdot x}{24} \geq 2$

Add $- 22 x$ and $24 x$ .

$\frac{2 x + 21}{24} \geq 2$

Step 3

Multiply both sides by $24$ .

$\frac{2 x + 21}{24} \cdot 24 \geq 2 \cdot 24$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{2 x + 21}{24} \cdot 24 \geq 2 \cdot 24$

Rewrite the expression.

$2 x + 21 \geq 2 \cdot 24$

Simplify the right side.

Multiply $2$ by $24$ .

$2 x + 21 \geq 48$

Step 5

Solve for $x$ .

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

Subtract $21$ from both sides of the inequality.

$2 x \geq 48 - 21$

Subtract $21$ from $48$ .

$2 x \geq 27$

Divide each term in $2 x \geq 27$ by $2$ and simplify.

Divide each term in $2 x \geq 27$ by $2$ .

$\frac{2 x}{2} \geq \frac{27}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{27}{2}$

Divide $x$ by $1$ .

$x \geq \frac{27}{2}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{27}{2}$

Interval Notation:

$[\frac{27}{2}, \infty)$

Solve for x (3-4x)/6-(2x-3)/8>=2-x

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