Find the Union (or) 6x-21=-17

$6 x - 21 \leq - 3$ , $14 x + 11 \geq - 17$

Simplify the first inequality.

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

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Add $21$ to both sides of the inequality.

$6 x \leq - 3 + 21$

Add $- 3$ and $21$ .

$6 x \leq 18$

Divide each term by $6$ and simplify.

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Divide each term in $6 x \leq 18$ by $6$ .

$\frac{6 x}{6} \leq \frac{18}{6}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$\frac{6 x}{6} \leq \frac{18}{6}$

Divide $x$ by $1$ .

$x \leq \frac{18}{6}$

Divide $18$ by $6$ .

$x \leq 3$

Simplify the second inequality.

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

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Subtract $11$ from both sides of the inequality.

$14 x \geq - 17 - 11$

Subtract $11$ from $- 17$ .

$14 x \geq - 28$

Divide each term by $14$ and simplify.

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Divide each term in $14 x \geq - 28$ by $14$ .

$\frac{14 x}{14} \geq \frac{- 28}{14}$

Cancel the common factor of $14$ .

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Cancel the common factor.

$\frac{14 x}{14} \geq \frac{- 28}{14}$

Divide $x$ by $1$ .

$x \geq \frac{- 28}{14}$

Divide $- 28$ by $14$ .

$x \geq - 2$

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

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Find the Union (or) 6x-21<=-3 , 14x+11>=-17

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