Solve 3/16(x-1)-5/12(x-4)=2/5(x-6)+3/4

$$\frac { 3 } { 16 } ( x - 1 ) - \frac { 5 } { 12 } ( x - 4 ) = \frac { 2 } { 5 } ( x - 6 ) + \frac { 3 } { 4 }$$

Solve for x

$$x = \frac{751}{151} = 4\frac{147}{151} \approx 4.973509934$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{16} by x-1.

$$\frac{3}{16}x+\frac{3}{16}\left(-1\right)-\frac{5}{12}\left(x-4\right)=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Multiply \frac{3}{16} and -1 to get -\frac{3}{16}.

$$\frac{3}{16}x-\frac{3}{16}-\frac{5}{12}\left(x-4\right)=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

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

$$\frac{3}{16}x-\frac{3}{16}-\frac{5}{12}x-\frac{5}{12}\left(-4\right)=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Express -\frac{5}{12}\left(-4\right) as a single fraction.

$$\frac{3}{16}x-\frac{3}{16}-\frac{5}{12}x+\frac{-5\left(-4\right)}{12}=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Multiply -5 and -4 to get 20.

$$\frac{3}{16}x-\frac{3}{16}-\frac{5}{12}x+\frac{20}{12}=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$\frac{3}{16}x-\frac{3}{16}-\frac{5}{12}x+\frac{5}{3}=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Combine \frac{3}{16}x and -\frac{5}{12}x to get -\frac{11}{48}x.

$$-\frac{11}{48}x-\frac{3}{16}+\frac{5}{3}=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Least common multiple of 16 and 3 is 48. Convert -\frac{3}{16} and \frac{5}{3} to fractions with denominator 48.

$$-\frac{11}{48}x-\frac{9}{48}+\frac{80}{48}=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Since -\frac{9}{48} and \frac{80}{48} have the same denominator, add them by adding their numerators.

$$-\frac{11}{48}x+\frac{-9+80}{48}=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Add -9 and 80 to get 71.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}\left(x-6\right)+\frac{3}{4}$$

Use the distributive property to multiply \frac{2}{5} by x-6.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}x+\frac{2}{5}\left(-6\right)+\frac{3}{4}$$

Express \frac{2}{5}\left(-6\right) as a single fraction.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}x+\frac{2\left(-6\right)}{5}+\frac{3}{4}$$

Multiply 2 and -6 to get -12.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}x+\frac{-12}{5}+\frac{3}{4}$$

Fraction \frac{-12}{5} can be rewritten as -\frac{12}{5} by extracting the negative sign.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}x-\frac{12}{5}+\frac{3}{4}$$

Least common multiple of 5 and 4 is 20. Convert -\frac{12}{5} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}x-\frac{48}{20}+\frac{15}{20}$$

Since -\frac{48}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}x+\frac{-48+15}{20}$$

Add -48 and 15 to get -33.

$$-\frac{11}{48}x+\frac{71}{48}=\frac{2}{5}x-\frac{33}{20}$$

Subtract \frac{2}{5}x from both sides.

$$-\frac{11}{48}x+\frac{71}{48}-\frac{2}{5}x=-\frac{33}{20}$$

Combine -\frac{11}{48}x and -\frac{2}{5}x to get -\frac{151}{240}x.

$$-\frac{151}{240}x+\frac{71}{48}=-\frac{33}{20}$$

Subtract \frac{71}{48} from both sides.

$$-\frac{151}{240}x=-\frac{33}{20}-\frac{71}{48}$$

Least common multiple of 20 and 48 is 240. Convert -\frac{33}{20} and \frac{71}{48} to fractions with denominator 240.

$$-\frac{151}{240}x=-\frac{396}{240}-\frac{355}{240}$$

Since -\frac{396}{240} and \frac{355}{240} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{151}{240}x=\frac{-396-355}{240}$$

Subtract 355 from -396 to get -751.

$$-\frac{151}{240}x=-\frac{751}{240}$$

Multiply both sides by -\frac{240}{151}, the reciprocal of -\frac{151}{240}.

$$x=-\frac{751}{240}\left(-\frac{240}{151}\right)$$

Multiply -\frac{751}{240} times -\frac{240}{151} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-751\left(-240\right)}{240\times 151}$$

Do the multiplications in the fraction \frac{-751\left(-240\right)}{240\times 151}.

$$x=\frac{180240}{36240}$$

Reduce the fraction \frac{180240}{36240} to lowest terms by extracting and canceling out 240.

$$x=\frac{751}{151}$$