Solve x-(1/4x+12)-3/5(x-1/4x-12)=48

$$x-( \frac{ 1 }{ 4 } x+12)- \frac{ 3 }{ 5 } (x- \frac{ 1 }{ 4 } x-12)=48$$

Solve for x

$$x=176$$

Steps for Solving Linear Equation

To find the opposite of \frac{1}{4}x+12, find the opposite of each term.

$$x-\frac{1}{4}x-12-\frac{3}{5}\left(x-\frac{1}{4}x-12\right)=48$$

Combine x and -\frac{1}{4}x to get \frac{3}{4}x.

$$\frac{3}{4}x-12-\frac{3}{5}\left(x-\frac{1}{4}x-12\right)=48$$

Combine x and -\frac{1}{4}x to get \frac{3}{4}x.

$$\frac{3}{4}x-12-\frac{3}{5}\left(\frac{3}{4}x-12\right)=48$$

Use the distributive property to multiply -\frac{3}{5} by \frac{3}{4}x-12.

$$\frac{3}{4}x-12-\frac{3}{5}\times \frac{3}{4}x-\frac{3}{5}\left(-12\right)=48$$

Multiply -\frac{3}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}x-12+\frac{-3\times 3}{5\times 4}x-\frac{3}{5}\left(-12\right)=48$$

Do the multiplications in the fraction \frac{-3\times 3}{5\times 4}.

$$\frac{3}{4}x-12+\frac{-9}{20}x-\frac{3}{5}\left(-12\right)=48$$

Fraction \frac{-9}{20} can be rewritten as -\frac{9}{20} by extracting the negative sign.

$$\frac{3}{4}x-12-\frac{9}{20}x-\frac{3}{5}\left(-12\right)=48$$

Express -\frac{3}{5}\left(-12\right) as a single fraction.

$$\frac{3}{4}x-12-\frac{9}{20}x+\frac{-3\left(-12\right)}{5}=48$$

Multiply -3 and -12 to get 36.

$$\frac{3}{4}x-12-\frac{9}{20}x+\frac{36}{5}=48$$

Combine \frac{3}{4}x and -\frac{9}{20}x to get \frac{3}{10}x.

$$\frac{3}{10}x-12+\frac{36}{5}=48$$

Convert -12 to fraction -\frac{60}{5}.

$$\frac{3}{10}x-\frac{60}{5}+\frac{36}{5}=48$$

Since -\frac{60}{5} and \frac{36}{5} have the same denominator, add them by adding their numerators.

$$\frac{3}{10}x+\frac{-60+36}{5}=48$$

Add -60 and 36 to get -24.

$$\frac{3}{10}x-\frac{24}{5}=48$$

Add \frac{24}{5} to both sides.

$$\frac{3}{10}x=48+\frac{24}{5}$$

Convert 48 to fraction \frac{240}{5}.

$$\frac{3}{10}x=\frac{240}{5}+\frac{24}{5}$$

Since \frac{240}{5} and \frac{24}{5} have the same denominator, add them by adding their numerators.

$$\frac{3}{10}x=\frac{240+24}{5}$$

Add 240 and 24 to get 264.

$$\frac{3}{10}x=\frac{264}{5}$$

Multiply both sides by \frac{10}{3}, the reciprocal of \frac{3}{10}.

$$x=\frac{264}{5}\times \frac{10}{3}$$

Multiply \frac{264}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{264\times 10}{5\times 3}$$

Do the multiplications in the fraction \frac{264\times 10}{5\times 3}.

$$x=\frac{2640}{15}$$

Divide 2640 by 15 to get 176.

$$x=176$$