Solve the System of Inequalities -4x+7<=35 and -5<=-4x+7

$- 4 x + 7 \leq 35$ and $- 5 \leq - 4 x + 7$

Simplify the first inequality.

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

Subtract $7$ from both sides of the inequality.

$- 4 x \leq 35 - 7$

Subtract $7$ from $35$ .

$- 4 x \leq 28$

Divide each term in $- 4 x \leq 28$ by $- 4$ and simplify.

Divide each term in $- 4 x \leq 28$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \geq \frac{28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \geq \frac{28}{- 4}$

Divide $x$ by $1$ .

$x \geq \frac{28}{- 4}$

Simplify the right side.

Divide $28$ by $- 4$ .

$x \geq - 7$

Simplify the second inequality.

Rewrite so $x$ is on the left side of the inequality.

$- 4 x + 7 \geq - 5$

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

Subtract $7$ from both sides of the inequality.

$- 4 x \geq - 5 - 7$

Subtract $7$ from $- 5$ .

$- 4 x \geq - 12$

Divide each term in $- 4 x \geq - 12$ by $- 4$ and simplify.

Divide each term in $- 4 x \geq - 12$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \leq \frac{- 12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \leq \frac{- 12}{- 4}$

Divide $x$ by $1$ .

$x \leq \frac{- 12}{- 4}$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$x \leq 3$

The intersection consists of the elements that are contained in both intervals.

$- 7 \leq x \leq 3$

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x \leq 3$

Interval Notation:

$[- 7, 3]$

Solve the System of Inequalities -4x+7<=35 and -5<=-4x+7

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