Solve the Inequality for x (6(x-3))/8>=3

$\frac{6 (x - 3)}{8} \geq 3$

Step 1

Cancel the common factor of $6$ and $8$ .

Factor $2$ out of $6 (x - 3)$ .

$\frac{2 (3 (x - 3))}{8} \geq 3$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{2 (3 (x - 3))}{2 (4)} \geq 3$

Cancel the common factor.

$\frac{2 (3 (x - 3))}{2 \cdot 4} \geq 3$

Rewrite the expression.

$\frac{3 (x - 3)}{4} \geq 3$

Step 2

Multiply both sides by $4$ .

$\frac{3 (x - 3)}{4} \cdot 4 \geq 3 \cdot 4$

Step 3

Simplify.

Simplify the left side.

Simplify $\frac{3 (x - 3)}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 (x - 3)}{4} \cdot 4 \geq 3 \cdot 4$

Rewrite the expression.

$3 (x - 3) \geq 3 \cdot 4$

Apply the distributive property.

$3 x + 3 \cdot - 3 \geq 3 \cdot 4$

Multiply $3$ by $- 3$ .

$3 x - 9 \geq 3 \cdot 4$

Simplify the right side.

Multiply $3$ by $4$ .

$3 x - 9 \geq 12$

Step 4

Solve for $x$ .

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

Add $9$ to both sides of the inequality.

$3 x \geq 12 + 9$

Add $12$ and $9$ .

$3 x \geq 21$

Divide each term in $3 x \geq 21$ by $3$ and simplify.

Divide each term in $3 x \geq 21$ by $3$ .

$\frac{3 x}{3} \geq \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{21}{3}$

Divide $x$ by $1$ .

$x \geq \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$x \geq 7$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 7$

Interval Notation:

$[7, \infty)$

Solve the Inequality for x (6(x-3))/8>=3

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