Solve for c 3(4c-5)-2c>0

$3 (4 c - 5) - 2 c > 0$

Step 1

Simplify $3 (4 c - 5) - 2 c$ .

Simplify each term.

Apply the distributive property.

$3 (4 c) + 3 \cdot - 5 - 2 c > 0$

Multiply $4$ by $3$ .

$12 c + 3 \cdot - 5 - 2 c > 0$

Multiply $3$ by $- 5$ .

$12 c - 15 - 2 c > 0$

$12 c - 15 - 2 c > 0$

Subtract $2 c$ from $12 c$ .

$10 c - 15 > 0$

$10 c - 15 > 0$

Step 2

Add $15$ to both sides of the inequality.

$10 c > 15$

Step 3

Divide each term in $10 c > 15$ by $10$ and simplify.

Divide each term in $10 c > 15$ by $10$ .

$\frac{10 c}{10} > \frac{15}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 c}{10} > \frac{15}{10}$

Divide $c$ by $1$ .

$c > \frac{15}{10}$

$c > \frac{15}{10}$

$c > \frac{15}{10}$

Simplify the right side.

Cancel the common factor of $15$ and $10$ .

Factor $5$ out of $15$ .

$c > \frac{5 (3)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$c > \frac{5 \cdot 3}{5 \cdot 2}$

Cancel the common factor.

$c > \frac{5 \cdot 3}{5 \cdot 2}$

Rewrite the expression.

$c > \frac{3}{2}$

$c > \frac{3}{2}$

$c > \frac{3}{2}$

$c > \frac{3}{2}$

$c > \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$c > \frac{3}{2}$

Interval Notation:

$(\frac{3}{2}, \infty)$

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