Solve for x 5x+1/3(3x+6)>14

$5 x + \frac{1}{3} (3 x + 6) > 14$

Step 1

Simplify $5 x + \frac{1}{3} \cdot (3 x + 6)$ .

Simplify each term.

Apply the distributive property.

$5 x + \frac{1}{3} (3 x) + \frac{1}{3} \cdot 6 > 14$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$5 x + \frac{1}{3} (3 (x)) + \frac{1}{3} \cdot 6 > 14$

Cancel the common factor.

$5 x + \frac{1}{3} (3 x) + \frac{1}{3} \cdot 6 > 14$

Rewrite the expression.

$5 x + x + \frac{1}{3} \cdot 6 > 14$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$5 x + x + \frac{1}{3} \cdot (3 (2)) > 14$

Cancel the common factor.

$5 x + x + \frac{1}{3} \cdot (3 \cdot 2) > 14$

Rewrite the expression.

$5 x + x + 2 > 14$

Add $5 x$ and $x$ .

$6 x + 2 > 14$

Step 2

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

Subtract $2$ from both sides of the inequality.

$6 x > 14 - 2$

Subtract $2$ from $14$ .

$6 x > 12$

Step 3

Divide each term in $6 x > 12$ by $6$ and simplify.

Divide each term in $6 x > 12$ by $6$ .

$\frac{6 x}{6} > \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} > \frac{12}{6}$

Divide $x$ by $1$ .

$x > \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$x > 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$

Solve for x 5x+1/3(3x+6)>14

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