Solve the System of Inequalities -34>=-4x+6 and -4x+6>=-42

$- 34 \geq - 4 x + 6$ and $- 4 x + 6 \geq - 42$

Step 1

Simplify the first inequality.

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

$- 4 x + 6 \leq - 34$

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

Subtract $6$ from both sides of the inequality.

$- 4 x \leq - 34 - 6$

Subtract $6$ from $- 34$ .

$- 4 x \leq - 40$

Divide each term in $- 4 x \leq - 40$ by $- 4$ and simplify.

Divide each term in $- 4 x \leq - 40$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \geq \frac{- 40}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \geq \frac{- 40}{- 4}$

Divide $x$ by $1$ .

$x \geq \frac{- 40}{- 4}$

Simplify the right side.

Divide $- 40$ by $- 4$ .

$x \geq 10$

Step 2

Simplify the second inequality.

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

Subtract $6$ from both sides of the inequality.

$- 4 x \geq - 42 - 6$

Subtract $6$ from $- 42$ .

$- 4 x \geq - 48$

Divide each term in $- 4 x \geq - 48$ by $- 4$ and simplify.

Divide each term in $- 4 x \geq - 48$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \leq \frac{- 48}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \leq \frac{- 48}{- 4}$

Divide $x$ by $1$ .

$x \leq \frac{- 48}{- 4}$

Simplify the right side.

Divide $- 48$ by $- 4$ .

$x \leq 12$

Step 3

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

$10 \leq x \leq 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$10 \leq x \leq 12$

Interval Notation:

$[10, 12]$

Step 5

Solve the System of Inequalities -34>=-4x+6 and -4x+6>=-42

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