Solve for x 1/2x+3<4x-7

$\frac{1}{2} x + 3 < 4 x - 7$

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

$\frac{x}{2} + 3 < 4 x - 7$

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

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

$\frac{x}{2} + 3 - 4 x < - 7$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x - 4 x \cdot 2$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} - 4 x \cdot 2}{2} + 3 < - 7$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - 4 x \cdot 2}{2} + 3 < - 7$

Factor $x$ out of $- 4 x \cdot 2$ .

$\frac{x \cdot 1 + x (- 4 \cdot 2)}{2} + 3 < - 7$

Factor $x$ out of $x \cdot 1 + x (- 4 \cdot 2)$ .

$\frac{x (1 - 4 \cdot 2)}{2} + 3 < - 7$

Multiply $- 4$ by $2$ .

$\frac{x (1 - 8)}{2} + 3 < - 7$

Subtract $8$ from $1$ .

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

Move $- 7$ to the left of $x$ .

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

Move the negative in front of the fraction.

$- \frac{7 x}{2} + 3 < - 7$

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

Subtract $3$ from both sides of the inequality.

$- \frac{7 x}{2} < - 7 - 3$

Subtract $3$ from $- 7$ .

$- \frac{7 x}{2} < - 10$

Divide each term in $- \frac{7 x}{2} < - 10$ by $- 1$ and simplify.

Divide each term in $- \frac{7 x}{2} < - 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{7 x}{2}}{- 1} > \frac{- 10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{7 x}{2}}{1} > \frac{- 10}{- 1}$

Divide $\frac{7 x}{2}$ by $1$ .

$\frac{7 x}{2} > \frac{- 10}{- 1}$

Simplify the right side.

Divide $- 10$ by $- 1$ .

$\frac{7 x}{2} > 10$

Multiply both sides by $2$ .

$\frac{7 x}{2} \cdot 2 > 10 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 x}{2} \cdot 2 > 10 \cdot 2$

Rewrite the expression.

$7 x > 10 \cdot 2$

Simplify the right side.

Multiply $10$ by $2$ .

$7 x > 20$

Divide each term in $7 x > 20$ by $7$ and simplify.

Divide each term in $7 x > 20$ by $7$ .

$\frac{7 x}{7} > \frac{20}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} > \frac{20}{7}$

Divide $x$ by $1$ .

$x > \frac{20}{7}$

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{20}{7}$

Interval Notation:

$(\frac{20}{7}, \infty)$

Solve for x 1/2x+3<4x-7

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