Solve the System of Inequalities -4x+10>=38 and -4x+10>-2

$- 4 x + 10 \geq 38$ and $- 4 x + 10 > - 2$

Step 1

Simplify the first inequality.

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

Subtract $10$ from both sides of the inequality.

$- 4 x \geq 38 - 10$ and $- 4 x + 10 > - 2$

Subtract $10$ from $38$ .

$- 4 x \geq 28$ and $- 4 x + 10 > - 2$

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

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

$\frac{- 4 x}{- 4} \leq \frac{28}{- 4}$ and $- 4 x + 10 > - 2$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \leq \frac{28}{- 4}$ and $- 4 x + 10 > - 2$

Divide $x$ by $1$ .

$x \leq \frac{28}{- 4}$ and $- 4 x + 10 > - 2$

Simplify the right side.

Divide $28$ by $- 4$ .

$x \leq - 7$ and $- 4 x + 10 > - 2$

Step 2

Simplify the second inequality.

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

Subtract $10$ from both sides of the inequality.

$x \leq - 7$ and $- 4 x > - 2 - 10$

Subtract $10$ from $- 2$ .

$x \leq - 7$ and $- 4 x > - 12$

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

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

$x \leq - 7$ and $\frac{- 4 x}{- 4} < \frac{- 12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$x \leq - 7$ and $\frac{- 4 x}{- 4} < \frac{- 12}{- 4}$

Divide $x$ by $1$ .

$x \leq - 7$ and $x < \frac{- 12}{- 4}$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$x \leq - 7$ and $x < 3$

Step 3

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

$x \leq - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 7$

Interval Notation:

$(- \infty, - 7]$

Step 5

Solve the System of Inequalities -4x+10>=38 and -4x+10>-2

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