Solve 1/3(x+2/5)-1/4(x/2+frac{2}{3})=(frac{x}{6}-frac{3}{7})

$$\frac{ 1 }{ 3 } (x+ \frac{ 2 }{ 5 } )- \frac{ 1 }{ 4 } ( \frac{ x }{ 2 } + \frac{ 2 }{ 3 } )=( \frac{ x }{ 6 } - \frac{ 3 }{ 7 } )$$

Solve for x

$$x = -\frac{332}{35} = -9\frac{17}{35} \approx -9.485714286$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 420, the least common multiple of 3,5,4,2,6,7.

$$140\left(x+\frac{2}{5}\right)-105\left(\frac{x}{2}+\frac{2}{3}\right)=70x-180$$

Use the distributive property to multiply 140 by x+\frac{2}{5}.

$$140x+140\times \frac{2}{5}-105\left(\frac{x}{2}+\frac{2}{3}\right)=70x-180$$

Express 140\times \frac{2}{5} as a single fraction.

$$140x+\frac{140\times 2}{5}-105\left(\frac{x}{2}+\frac{2}{3}\right)=70x-180$$

Multiply 140 and 2 to get 280.

$$140x+\frac{280}{5}-105\left(\frac{x}{2}+\frac{2}{3}\right)=70x-180$$

Divide 280 by 5 to get 56.

$$140x+56-105\left(\frac{x}{2}+\frac{2}{3}\right)=70x-180$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x}{2} times \frac{3}{3}. Multiply \frac{2}{3} times \frac{2}{2}.

$$140x+56-105\left(\frac{3x}{6}+\frac{2\times 2}{6}\right)=70x-180$$

Since \frac{3x}{6} and \frac{2\times 2}{6} have the same denominator, add them by adding their numerators.

$$140x+56-105\times \frac{3x+2\times 2}{6}=70x-180$$

Do the multiplications in 3x+2\times 2.

$$140x+56-105\times \frac{3x+4}{6}=70x-180$$

Express 105\times \frac{3x+4}{6} as a single fraction.

$$140x+56-\frac{105\left(3x+4\right)}{6}=70x-180$$

Use the distributive property to multiply 105 by 3x+4.

$$140x+56-\frac{315x+420}{6}=70x-180$$

Divide each term of 315x+420 by 6 to get \frac{105}{2}x+70.

$$140x+56-\left(\frac{105}{2}x+70\right)=70x-180$$

To find the opposite of \frac{105}{2}x+70, find the opposite of each term.

$$140x+56-\frac{105}{2}x-70=70x-180$$

Combine 140x and -\frac{105}{2}x to get \frac{175}{2}x.

$$\frac{175}{2}x+56-70=70x-180$$

Subtract 70 from 56 to get -14.

$$\frac{175}{2}x-14=70x-180$$

Subtract 70x from both sides.

$$\frac{175}{2}x-14-70x=-180$$

Combine \frac{175}{2}x and -70x to get \frac{35}{2}x.

$$\frac{35}{2}x-14=-180$$

Add 14 to both sides.

$$\frac{35}{2}x=-180+14$$

Add -180 and 14 to get -166.

$$\frac{35}{2}x=-166$$

Multiply both sides by \frac{2}{35}, the reciprocal of \frac{35}{2}.

$$x=-166\times \frac{2}{35}$$

Express -166\times \frac{2}{35} as a single fraction.

$$x=\frac{-166\times 2}{35}$$

Multiply -166 and 2 to get -332.

$$x=\frac{-332}{35}$$

Fraction \frac{-332}{35} can be rewritten as -\frac{332}{35} by extracting the negative sign.

$$x=-\frac{332}{35}$$