Solve left(3/4x-1/6right)/frac{5{24}}=15x/2-frac{1}{2}

$$\frac{ \left( \frac{ 3 }{ 4 } x- \frac{ 1 }{ 6 } \right) }{ \frac{ 5 }{ 24 } } = \frac{ 15x }{ 2 } - \frac{ 1 }{ 2 }$$

Solve for x

$$x=-\frac{1}{13}\approx -0.076923077$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{\frac{3}{4}x-\frac{1}{6}}{\frac{5}{24}}=15x-1$$

Divide each term of \frac{3}{4}x-\frac{1}{6} by \frac{5}{24} to get \frac{\frac{3}{4}x}{\frac{5}{24}}+\frac{-\frac{1}{6}}{\frac{5}{24}}.

$$2\left(\frac{\frac{3}{4}x}{\frac{5}{24}}+\frac{-\frac{1}{6}}{\frac{5}{24}}\right)=15x-1$$

Divide \frac{3}{4}x by \frac{5}{24} to get \frac{18}{5}x.

$$2\left(\frac{18}{5}x+\frac{-\frac{1}{6}}{\frac{5}{24}}\right)=15x-1$$

Divide -\frac{1}{6} by \frac{5}{24} by multiplying -\frac{1}{6} by the reciprocal of \frac{5}{24}.

$$2\left(\frac{18}{5}x-\frac{1}{6}\times \frac{24}{5}\right)=15x-1$$

Multiply -\frac{1}{6} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$2\left(\frac{18}{5}x+\frac{-24}{6\times 5}\right)=15x-1$$

Do the multiplications in the fraction \frac{-24}{6\times 5}.

$$2\left(\frac{18}{5}x+\frac{-24}{30}\right)=15x-1$$

Reduce the fraction \frac{-24}{30} to lowest terms by extracting and canceling out 6.

$$2\left(\frac{18}{5}x-\frac{4}{5}\right)=15x-1$$

Use the distributive property to multiply 2 by \frac{18}{5}x-\frac{4}{5}.

$$2\times \frac{18}{5}x+2\left(-\frac{4}{5}\right)=15x-1$$

Express 2\times \frac{18}{5} as a single fraction.

$$\frac{2\times 18}{5}x+2\left(-\frac{4}{5}\right)=15x-1$$

Multiply 2 and 18 to get 36.

$$\frac{36}{5}x+2\left(-\frac{4}{5}\right)=15x-1$$

Express 2\left(-\frac{4}{5}\right) as a single fraction.

$$\frac{36}{5}x+\frac{2\left(-4\right)}{5}=15x-1$$

Multiply 2 and -4 to get -8.

$$\frac{36}{5}x+\frac{-8}{5}=15x-1$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{36}{5}x-\frac{8}{5}=15x-1$$

Subtract 15x from both sides.

$$\frac{36}{5}x-\frac{8}{5}-15x=-1$$

Combine \frac{36}{5}x and -15x to get -\frac{39}{5}x.

$$-\frac{39}{5}x-\frac{8}{5}=-1$$

Add \frac{8}{5} to both sides.

$$-\frac{39}{5}x=-1+\frac{8}{5}$$

Convert -1 to fraction -\frac{5}{5}.

$$-\frac{39}{5}x=-\frac{5}{5}+\frac{8}{5}$$

Since -\frac{5}{5} and \frac{8}{5} have the same denominator, add them by adding their numerators.

$$-\frac{39}{5}x=\frac{-5+8}{5}$$

Add -5 and 8 to get 3.

$$-\frac{39}{5}x=\frac{3}{5}$$

Multiply both sides by -\frac{5}{39}, the reciprocal of -\frac{39}{5}.

$$x=\frac{3}{5}\left(-\frac{5}{39}\right)$$

Multiply \frac{3}{5} times -\frac{5}{39} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\left(-5\right)}{5\times 39}$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{5\times 39}.

$$x=\frac{-15}{195}$$

Reduce the fraction \frac{-15}{195} to lowest terms by extracting and canceling out 15.

$$x=-\frac{1}{13}$$