Solve for x (4x-1)/x=3x

$\frac{4 x - 1}{x} = 3 x$

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.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Multiply each term in $\frac{4 x - 1}{x} = 3 x$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{4 x - 1}{x} = 3 x$ by $x$ .

$\frac{4 x - 1}{x} x = 3 x \cdot x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{4 x - 1}{x} x = 3 x \cdot x$

Rewrite the expression.

$4 x - 1 = 3 x \cdot x$

Simplify the right side.

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

Move $x$ .

$4 x - 1 = 3 (x \cdot x)$

Multiply $x$ by $x$ .

$4 x - 1 = 3 x^{2}$

Solve the equation.

Subtract $3 x^{2}$ from both sides of the equation.

$4 x - 1 - 3 x^{2} = 0$

Factor the left side of the equation.

Factor $- 1$ out of $4 x - 1 - 3 x^{2}$ .

Reorder the expression.

Move $- 1$ .

$4 x - 3 x^{2} - 1 = 0$

Reorder $4 x$ and $- 3 x^{2}$ .

$- 3 x^{2} + 4 x - 1 = 0$

Factor $- 1$ out of $- 3 x^{2}$ .

$- (3 x^{2}) + 4 x - 1 = 0$

Factor $- 1$ out of $4 x$ .

$- (3 x^{2}) - (- 4 x) - 1 = 0$

Rewrite $- 1$ as $- 1 (1)$ .

$- (3 x^{2}) - (- 4 x) - 1 \cdot 1 = 0$

Factor $- 1$ out of $- (3 x^{2}) - (- 4 x)$ .

$- (3 x^{2} - 4 x) - 1 \cdot 1 = 0$

Factor $- 1$ out of $- (3 x^{2} - 4 x) - 1 (1)$ .

$- (3 x^{2} - 4 x + 1) = 0$

Factor.

Factor by grouping.

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 $a \cdot c = 3 \cdot 1 = 3$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 x$ .

$- (3 x^{2} - 4 x + 1) = 0$

Rewrite $- 4$ as $- 1$ plus $- 3$

$- (3 x^{2} + (- 1 - 3) x + 1) = 0$

Apply the distributive property.

$- (3 x^{2} - 1 x - 3 x + 1) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((3 x^{2} - 1 x) - 3 x + 1) = 0$

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

$- (x (3 x - 1) - (3 x - 1)) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$- ((3 x - 1) (x - 1)) = 0$

Remove unnecessary parentheses.

$- (3 x - 1) (x - 1) = 0$

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

$3 x - 1 = 0$

$x - 1 = 0$

Set $3 x - 1$ equal to $0$ and solve for $x$ .

Set $3 x - 1$ equal to $0$ .

$3 x - 1 = 0$

Solve $3 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$3 x = 1$

Divide each term in $3 x = 1$ by $3$ and simplify.

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3}$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $- (3 x - 1) (x - 1) = 0$ true.

$x = \frac{1}{3}, 1$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}, 1$

Decimal Form:

$x = 0.\overline{3}, 1$

Solve for x (4x-1)/x=3x

Related Questions

Support LCMGCF.com by disabling your adblocker.