Solve the Inequality for x 7(3-x)>=5

$7 (3 - x) \geq 5$

Divide each term in $7 (3 - x) \geq 5$ by $7$ and simplify.

Divide each term in $7 (3 - x) \geq 5$ by $7$ .

$\frac{7 (3 - x)}{7} \geq \frac{5}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (3 - x)}{7} \geq \frac{5}{7}$

Divide $3 - x$ by $1$ .

$3 - x \geq \frac{5}{7}$

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

Subtract $3$ from both sides of the inequality.

$- x \geq \frac{5}{7} - 3$

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

$- x \geq \frac{5}{7} - 3 \cdot \frac{7}{7}$

Combine $- 3$ and $\frac{7}{7}$ .

$- x \geq \frac{5}{7} + \frac{- 3 \cdot 7}{7}$

Combine the numerators over the common denominator.

$- x \geq \frac{5 - 3 \cdot 7}{7}$

Simplify the numerator.

Multiply $- 3$ by $7$ .

$- x \geq \frac{5 - 21}{7}$

Subtract $21$ from $5$ .

$- x \geq \frac{- 16}{7}$

Move the negative in front of the fraction.

$- x \geq - \frac{16}{7}$

Divide each term in $- x \geq - \frac{16}{7}$ by $- 1$ and simplify.

Divide each term in $- x \geq - \frac{16}{7}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{- \frac{16}{7}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{- \frac{16}{7}}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{- \frac{16}{7}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \leq \frac{\frac{16}{7}}{1}$

Divide $\frac{16}{7}$ by $1$ .

$x \leq \frac{16}{7}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{16}{7}$

Interval Notation:

$(- \infty, \frac{16}{7}]$

Solve the Inequality for x 7(3-x)>=5

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