Solve the System of Inequalities 5x+2>=37 or -7-x>-2

$5 x + 2 \geq 37$ or $- 7 - x > - 2$

Simplify the first inequality.

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

Subtract $2$ from both sides of the inequality.

$5 x \geq 37 - 2$ or $- 7 - x > - 2$

Subtract $2$ from $37$ .

$5 x \geq 35$ or $- 7 - x > - 2$

Divide each term in $5 x \geq 35$ by $5$ and simplify.

Divide each term in $5 x \geq 35$ by $5$ .

$\frac{5 x}{5} \geq \frac{35}{5}$ or $- 7 - x > - 2$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{35}{5}$ or $- 7 - x > - 2$

Divide $x$ by $1$ .

$x \geq \frac{35}{5}$ or $- 7 - x > - 2$

Simplify the right side.

Divide $35$ by $5$ .

$x \geq 7$ or $- 7 - x > - 2$

Simplify the second inequality.

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

Add $7$ to both sides of the inequality.

$x \geq 7$ or $- x > - 2 + 7$

Add $- 2$ and $7$ .

$x \geq 7$ or $- x > 5$

Divide each term in $- x > 5$ by $- 1$ and simplify.

Divide each term in $- x > 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \geq 7$ or $\frac{- x}{- 1} < \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$x \geq 7$ or $\frac{x}{1} < \frac{5}{- 1}$

Divide $x$ by $1$ .

$x \geq 7$ or $x < \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$x \geq 7$ or $x < - 5$

The union consists of all of the elements that are contained in each interval.

$x < - 5$ or $x \geq 7$

The result can be shown in multiple forms.

Inequality Form:

$x < - 5 or x \geq 7$

Interval Notation:

$(- \infty, - 5) \cup [7, \infty)$

Solve the System of Inequalities 5x+2>=37 or -7-x>-2

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