Solve the System of Inequalities -7x+1>=22 or -10x+41>=81

$- 7 x + 1 \geq 22$ or $- 10 x + 41 \geq 81$

Simplify the first inequality.

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

Subtract $1$ from both sides of the inequality.

$- 7 x \geq 22 - 1$

Subtract $1$ from $22$ .

$- 7 x \geq 21$

Divide each term in $- 7 x \geq 21$ by $- 7$ and simplify.

Divide each term in $- 7 x \geq 21$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} \leq \frac{21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} \leq \frac{21}{- 7}$

Divide $x$ by $1$ .

$x \leq \frac{21}{- 7}$

Simplify the right side.

Divide $21$ by $- 7$ .

$x \leq - 3$

Simplify the second inequality.

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

Subtract $41$ from both sides of the inequality.

$- 10 x \geq 81 - 41$

Subtract $41$ from $81$ .

$- 10 x \geq 40$

Divide each term in $- 10 x \geq 40$ by $- 10$ and simplify.

Divide each term in $- 10 x \geq 40$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 x}{- 10} \leq \frac{40}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} \leq \frac{40}{- 10}$

Divide $x$ by $1$ .

$x \leq \frac{40}{- 10}$

Simplify the right side.

Divide $40$ by $- 10$ .

$x \leq - 4$

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

$x \leq - 3$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 3$

Interval Notation:

$(- \infty, - 3]$

Solve the System of Inequalities -7x+1>=22 or -10x+41>=81

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