Evaluate 21x+7>2(9x-8)+3-7x

$21 x + 7 > 2 (9 x - 8) + 3 - 7 x$

Step 1

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

$2 (9 x - 8) + 3 - 7 x < 21 x + 7$

Step 2

Simplify $2 (9 x - 8) + 3 - 7 x$ .

Simplify each term.

Apply the distributive property.

$2 (9 x) + 2 \cdot - 8 + 3 - 7 x < 21 x + 7$

Multiply $9$ by $2$ .

$18 x + 2 \cdot - 8 + 3 - 7 x < 21 x + 7$

Multiply $2$ by $- 8$ .

$18 x - 16 + 3 - 7 x < 21 x + 7$

Simplify by adding terms.

Subtract $7 x$ from $18 x$ .

$11 x - 16 + 3 < 21 x + 7$

Add $- 16$ and $3$ .

$11 x - 13 < 21 x + 7$

Step 3

Move all terms containing $x$ to the left side of the inequality.

Subtract $21 x$ from both sides of the inequality.

$11 x - 13 - 21 x < 7$

Subtract $21 x$ from $11 x$ .

$- 10 x - 13 < 7$

Step 4

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

Add $13$ to both sides of the inequality.

$- 10 x < 7 + 13$

Add $7$ and $13$ .

$- 10 x < 20$

Step 5

Divide each term in $- 10 x < 20$ by $- 10$ and simplify.

Divide each term in $- 10 x < 20$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 x}{- 10} > \frac{20}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} > \frac{20}{- 10}$

Divide $x$ by $1$ .

$x > \frac{20}{- 10}$

Simplify the right side.

Divide $20$ by $- 10$ .

$x > - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - 2$

Interval Notation:

$(- 2, \infty)$

Evaluate 21x+7>2(9x-8)+3-7x

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