Graph the Union (or) 4x+2>14 , -21x+1>22

$4 x + 2 > 14$ , $- 21 x + 1 > 22$

Step 1

Simplify the first inequality.

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

Subtract $2$ from both sides of the inequality.

$4 x > 14 - 2$ or $- 21 x + 1 > 22$

Subtract $2$ from $14$ .

$4 x > 12$ or $- 21 x + 1 > 22$

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

Divide each term in $4 x > 12$ by $4$ .

$\frac{4 x}{4} > \frac{12}{4}$ or $- 21 x + 1 > 22$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{12}{4}$ or $- 21 x + 1 > 22$

Divide $x$ by $1$ .

$x > \frac{12}{4}$ or $- 21 x + 1 > 22$

Simplify the right side.

Divide $12$ by $4$ .

$x > 3$ or $- 21 x + 1 > 22$

Step 2

Simplify the second inequality.

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

Subtract $1$ from both sides of the inequality.

$x > 3$ or $- 21 x > 22 - 1$

Subtract $1$ from $22$ .

$x > 3$ or $- 21 x > 21$

Divide each term in $- 21 x > 21$ by $- 21$ and simplify.

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

$x > 3$ or $\frac{- 21 x}{- 21} < \frac{21}{- 21}$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$x > 3$ or $\frac{- 21 x}{- 21} < \frac{21}{- 21}$

Divide $x$ by $1$ .

$x > 3$ or $x < \frac{21}{- 21}$

Simplify the right side.

Divide $21$ by $- 21$ .

$x > 3$ or $x < - 1$

Step 3

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

$x < - 1$ or $x > 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 1 or x > 3$

Interval Notation:

$(- \infty, - 1) \cup (3, \infty)$

Step 5

Graph the Union (or) 4x+2>14 , -21x+1>22

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