Solve the System of Inequalities -4x+1<=21 and 5x+2<22

$- 4 x + 1 \leq 21$ and $5 x + 2 < 22$

Step 1

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.

$- 4 x \leq 21 - 1$ and $5 x + 2 < 22$

Subtract $1$ from $21$ .

$- 4 x \leq 20$ and $5 x + 2 < 22$

Divide each term in $- 4 x \leq 20$ by $- 4$ and simplify.

Divide each term in $- 4 x \leq 20$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \geq \frac{20}{- 4}$ and $5 x + 2 < 22$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \geq \frac{20}{- 4}$ and $5 x + 2 < 22$

Divide $x$ by $1$ .

$x \geq \frac{20}{- 4}$ and $5 x + 2 < 22$

Simplify the right side.

Divide $20$ by $- 4$ .

$x \geq - 5$ and $5 x + 2 < 22$

Step 2

Simplify the second inequality.

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

Subtract $2$ from both sides of the inequality.

$x \geq - 5$ and $5 x < 22 - 2$

Subtract $2$ from $22$ .

$x \geq - 5$ and $5 x < 20$

Divide each term in $5 x < 20$ by $5$ and simplify.

Divide each term in $5 x < 20$ by $5$ .

$x \geq - 5$ and $\frac{5 x}{5} < \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$x \geq - 5$ and $\frac{5 x}{5} < \frac{20}{5}$

Divide $x$ by $1$ .

$x \geq - 5$ and $x < \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x \geq - 5$ and $x < 4$

Step 3

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

$- 5 \leq x < 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x < 4$

Interval Notation:

$[- 5, 4)$

Step 5

Solve the System of Inequalities -4x+1<=21 and 5x+2<22

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