Solve for x 7-6x<2x+89

$7 - 6 x < 2 x + 89$

Step 1

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

Subtract $2 x$ from both sides of the inequality.

$7 - 6 x - 2 x < 89$

Subtract $2 x$ from $- 6 x$ .

$7 - 8 x < 89$

Step 2

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

Subtract $7$ from both sides of the inequality.

$- 8 x < 89 - 7$

Subtract $7$ from $89$ .

$- 8 x < 82$

Step 3

Divide each term in $- 8 x < 82$ by $- 8$ and simplify.

Divide each term in $- 8 x < 82$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} > \frac{82}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} > \frac{82}{- 8}$

Divide $x$ by $1$ .

$x > \frac{82}{- 8}$

Simplify the right side.

Cancel the common factor of $82$ and $- 8$ .

Factor $2$ out of $82$ .

$x > \frac{2 (41)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$x > \frac{2 \cdot 41}{2 \cdot - 4}$

Cancel the common factor.

$x > \frac{2 \cdot 41}{2 \cdot - 4}$

Rewrite the expression.

$x > \frac{41}{- 4}$

Move the negative in front of the fraction.

$x > - \frac{41}{4}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{41}{4}$

Interval Notation:

$(- \frac{41}{4}, \infty)$

Solve for x 7-6x<2x+89

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