Solve for x (5x-4)/2-7>4x-3

$\frac{5 x - 4}{2} - 7 > 4 x - 3$

Simplify $\frac{5 x - 4}{2} - 7$ .

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

$\frac{5 x - 4}{2} - 7 \cdot \frac{2}{2} > 4 x - 3$

Simplify terms.

Combine $- 7$ and $\frac{2}{2}$ .

$\frac{5 x - 4}{2} + \frac{- 7 \cdot 2}{2} > 4 x - 3$

Combine the numerators over the common denominator.

$\frac{5 x - 4 - 7 \cdot 2}{2} > 4 x - 3$

Simplify the numerator.

Multiply $- 7$ by $2$ .

$\frac{5 x - 4 - 14}{2} > 4 x - 3$

Subtract $14$ from $- 4$ .

$\frac{5 x - 18}{2} > 4 x - 3$

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

Subtract $4 x$ from both sides of the inequality.

$\frac{5 x - 18}{2} - 4 x > - 3$

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x - 18}{2} - 4 x \cdot \frac{2}{2} > - 3$

Combine $- 4 x$ and $\frac{2}{2}$ .

$\frac{5 x - 18}{2} + \frac{- 4 x \cdot 2}{2} > - 3$

Combine the numerators over the common denominator.

$\frac{5 x - 18 - 4 x \cdot 2}{2} > - 3$

Simplify the numerator.

Multiply $2$ by $- 4$ .

$\frac{5 x - 18 - 8 x}{2} > - 3$

Subtract $8 x$ from $5 x$ .

$\frac{- 3 x - 18}{2} > - 3$

Factor $3$ out of $- 3 x - 18$ .

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) - 18}{2} > - 3$

Factor $3$ out of $- 18$ .

$\frac{3 (- x) + 3 (- 6)}{2} > - 3$

Factor $3$ out of $3 (- x) + 3 (- 6)$ .

$\frac{3 (- x - 6)}{2} > - 3$

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

$\frac{3 (- (x) - 6)}{2} > - 3$

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{3 (- (x) - 1 (6))}{2} > - 3$

Factor $- 1$ out of $- (x) - 1 (6)$ .

$\frac{3 (- (x + 6))}{2} > - 3$

Rewrite $- (x + 6)$ as $- 1 (x + 6)$ .

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

Move the negative in front of the fraction.

$- \frac{3 (x + 6)}{2} > - 3$

Divide each term in $- \frac{3 (x + 6)}{2} > - 3$ by $- 1$ and simplify.

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $\frac{3 (x + 6)}{2}$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 1$ .

$\frac{3 (x + 6)}{2} < 3$

Multiply both sides by $2$ .

$\frac{3 (x + 6)}{2} \cdot 2 < 3 \cdot 2$

Simplify.

Simplify the left side.

Simplify $\frac{3 (x + 6)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 (x + 6)}{2} \cdot 2 < 3 \cdot 2$

Rewrite the expression.

$3 (x + 6) < 3 \cdot 2$

Apply the distributive property.

$3 x + 3 \cdot 6 < 3 \cdot 2$

Multiply $3$ by $6$ .

$3 x + 18 < 3 \cdot 2$

Simplify the right side.

Multiply $3$ by $2$ .

$3 x + 18 < 6$

Solve for $x$ .

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

Subtract $18$ from both sides of the inequality.

$3 x < 6 - 18$

Subtract $18$ from $6$ .

$3 x < - 12$

Divide each term in $3 x < - 12$ by $3$ and simplify.

Divide each term in $3 x < - 12$ by $3$ .

$\frac{3 x}{3} < \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 12}{3}$

Divide $x$ by $1$ .

$x < \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$x < - 4$

The result can be shown in multiple forms.

Inequality Form:

$x < - 4$

Interval Notation:

$(- \infty, - 4)$

Solve for x (5x-4)/2-7>4x-3

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