Solve for x 7x+9>=13x+1>3x+2

$7 x + 9 \geq 13 x + 1 > 3 x + 2$

Step 1

Solve $7 x + 9 \geq 13 x + 1$ for $x$ .

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

Subtract $13 x$ from both sides of the inequality.

$7 x + 9 - 13 x \geq 1$

Subtract $13 x$ from $7 x$ .

$- 6 x + 9 \geq 1$

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

Subtract $9$ from both sides of the inequality.

$- 6 x \geq 1 - 9$

Subtract $9$ from $1$ .

$- 6 x \geq - 8$

Divide each term in $- 6 x \geq - 8$ by $- 6$ and simplify.

Divide each term in $- 6 x \geq - 8$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 x}{- 6} \leq \frac{- 8}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} \leq \frac{- 8}{- 6}$

Divide $x$ by $1$ .

$x \leq \frac{- 8}{- 6}$

Simplify the right side.

Cancel the common factor of $- 8$ and $- 6$ .

Factor $- 2$ out of $- 8$ .

$x \leq \frac{- 2 (4)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$x \leq \frac{- 2 \cdot 4}{- 2 \cdot 3}$

Cancel the common factor.

$x \leq \frac{- 2 \cdot 4}{- 2 \cdot 3}$

Rewrite the expression.

$x \leq \frac{4}{3}$

Step 2

Solve $13 x + 1 > 3 x + 2$ for $x$ .

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

Subtract $3 x$ from both sides of the inequality.

$13 x + 1 - 3 x > 2$

Subtract $3 x$ from $13 x$ .

$10 x + 1 > 2$

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

Subtract $1$ from both sides of the inequality.

$10 x > 2 - 1$

Subtract $1$ from $2$ .

$10 x > 1$

Divide each term in $10 x > 1$ by $10$ and simplify.

Divide each term in $10 x > 1$ by $10$ .

$\frac{10 x}{10} > \frac{1}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} > \frac{1}{10}$

Divide $x$ by $1$ .

$x > \frac{1}{10}$

Step 3

Find the intersection of $x \leq \frac{4}{3}$ and $x > \frac{1}{10}$ .

$\frac{1}{10} < x \leq \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$\frac{1}{10} < x \leq \frac{4}{3}$

Interval Notation:

$(\frac{1}{10}, \frac{4}{3}]$

Step 5

Solve for x 7x+9>=13x+1>3x+2

Related Questions

Support LCMGCF.com by disabling your adblocker.