Solve the Inequality for g 10g-(8g+9)<-g+8+6

$10 g - (8 g + 9) < - g + 8 + 6$

Simplify $10 g - (8 g + 9)$ .

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Simplify each term.

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Apply the distributive property.

$10 g - (8 g) - 1 \cdot 9 < - g + 8 + 6$

Multiply $8$ by $- 1$ .

$10 g - 8 g - 1 \cdot 9 < - g + 8 + 6$

Multiply $- 1$ by $9$ .

$10 g - 8 g - 9 < - g + 8 + 6$

Subtract $8 g$ from $10 g$ .

$2 g - 9 < - g + 8 + 6$

Add $8$ and $6$ .

$2 g - 9 < - g + 14$

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

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Add $g$ to both sides of the inequality.

$2 g - 9 + g < 14$

Add $2 g$ and $g$ .

$3 g - 9 < 14$

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

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Add $9$ to both sides of the inequality.

$3 g < 14 + 9$

Add $14$ and $9$ .

$3 g < 23$

Divide each term in $3 g < 23$ by $3$ and simplify.

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Divide each term in $3 g < 23$ by $3$ .

$\frac{3 g}{3} < \frac{23}{3}$

Simplify the left side.

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Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 g}{3} < \frac{23}{3}$

Divide $g$ by $1$ .

$g < \frac{23}{3}$

The result can be shown in multiple forms.

Inequality Form:

$g < \frac{23}{3}$

Interval Notation:

$(- \infty, \frac{23}{3})$