Solve for x 2x+12/x=11

$2 x + \frac{12}{x} = 11$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x, 1$

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $2 x + \frac{12}{x} = 11$ by $x$ to eliminate the fractions.

Multiply each term in $2 x + \frac{12}{x} = 11$ by $x$ .

$2 x \cdot x + \frac{12}{x} x = 11 x$

Simplify the left side.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + \frac{12}{x} x = 11 x$

Multiply $x$ by $x$ .

$2 x^{2} + \frac{12}{x} x = 11 x$

Cancel the common factor of $x$ .

Cancel the common factor.

$2 x^{2} + \frac{12}{x} x = 11 x$

Rewrite the expression.

$2 x^{2} + 12 = 11 x$

Step 3

Solve the equation.

Subtract $11 x$ from both sides of the equation.

$2 x^{2} + 12 - 11 x = 0$

Factor by grouping.

Reorder terms.

$2 x^{2} - 11 x + 12 = 0$

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 12 = 24$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$2 x^{2} - 11 x + 12 = 0$

Rewrite $- 11$ as $- 3$ plus $- 8$

$2 x^{2} + (- 3 - 8) x + 12 = 0$

Apply the distributive property.

$2 x^{2} - 3 x - 8 x + 12 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x) - 8 x + 12 = 0$

Factor out the greatest common factor (GCF) from each group.

$x (2 x - 3) - 4 (2 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (x - 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 3 = 0$

$x - 4 = 0$

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $(2 x - 3) (x - 4) = 0$ true.

$x = \frac{3}{2}, 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}, 4$

Decimal Form:

$x = 1.5, 4$

Mixed Number Form:

$x = 1 \frac{1}{2}, 4$

Solve for x 2x+12/x=11

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