Solve the Inequality for g 7g-24>6(4-5g)

$7 g - 24 > 6 (4 - 5 g)$

Step 1

Simplify $6 (4 - 5 g)$ .

Rewrite.

$7 g - 24 > 0 + 0 + 6 (4 - 5 g)$

Simplify by adding zeros.

$7 g - 24 > 6 (4 - 5 g)$

Apply the distributive property.

$7 g - 24 > 6 \cdot 4 + 6 (- 5 g)$

Multiply.

Multiply $6$ by $4$ .

$7 g - 24 > 24 + 6 (- 5 g)$

Multiply $- 5$ by $6$ .

$7 g - 24 > 24 - 30 g$

Step 2

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

Add $30 g$ to both sides of the inequality.

$7 g - 24 + 30 g > 24$

Add $7 g$ and $30 g$ .

$37 g - 24 > 24$

Step 3

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

Add $24$ to both sides of the inequality.

$37 g > 24 + 24$

Add $24$ and $24$ .

$37 g > 48$

Step 4

Divide each term in $37 g > 48$ by $37$ and simplify.

Divide each term in $37 g > 48$ by $37$ .

$\frac{37 g}{37} > \frac{48}{37}$

Simplify the left side.

Cancel the common factor of $37$ .

Cancel the common factor.

$\frac{37 g}{37} > \frac{48}{37}$

Divide $g$ by $1$ .

$g > \frac{48}{37}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$g > \frac{48}{37}$

Interval Notation:

$(\frac{48}{37}, \infty)$