Solve for z 6z-7>8z+2

$6 z - 7 > 8 z + 2$

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

Subtract $8 z$ from both sides of the inequality.

$6 z - 7 - 8 z > 2$

Subtract $8 z$ from $6 z$ .

$- 2 z - 7 > 2$

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

Add $7$ to both sides of the inequality.

$- 2 z > 2 + 7$

Add $2$ and $7$ .

$- 2 z > 9$

Divide each term in $- 2 z > 9$ by $- 2$ and simplify.

Divide each term in $- 2 z > 9$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 z}{- 2} < \frac{9}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 z}{- 2} < \frac{9}{- 2}$

Divide $z$ by $1$ .

$z < \frac{9}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$z < - \frac{9}{2}$

The result can be shown in multiple forms.

Inequality Form:

$z < - \frac{9}{2}$

Interval Notation:

$(- \infty, - \frac{9}{2})$

Solve for z 6z-7>8z+2

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