Solve the System of @WORD 5+x>=3x-7>5x+13

$5 + x \geq 3 x - 7 > 5 x + 13$

Step 1

Solve $5 + x \geq 3 x - 7$ for $x$ .

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

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

$5 + x - 3 x \geq - 7$

Subtract $3 x$ from $x$ .

$5 - 2 x \geq - 7$

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

Subtract $5$ from both sides of the inequality.

$- 2 x \geq - 7 - 5$

Subtract $5$ from $- 7$ .

$- 2 x \geq - 12$

Divide each term in $- 2 x \geq - 12$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq - 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{- 12}{- 2}$

Divide $x$ by $1$ .

$x \leq \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$x \leq 6$

Step 2

Solve $3 x - 7 > 5 x + 13$ for $x$ .

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

Subtract $5 x$ from both sides of the inequality.

$3 x - 7 - 5 x > 13$

Subtract $5 x$ from $3 x$ .

$- 2 x - 7 > 13$

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

Add $7$ to both sides of the inequality.

$- 2 x > 13 + 7$

Add $13$ and $7$ .

$- 2 x > 20$

Divide each term in $- 2 x > 20$ by $- 2$ and simplify.

Divide each term in $- 2 x > 20$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{20}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{20}{- 2}$

Divide $x$ by $1$ .

$x < \frac{20}{- 2}$

Simplify the right side.

Divide $20$ by $- 2$ .

$x < - 10$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 10$

Interval Notation:

$(- \infty, - 10)$

Step 4

Solve the System of @WORD 5+x>=3x-7>5x+13

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