Solve 5/6[x-1/3]+7/6[x/5-frac{1}{7}]=4frac{8}{9}

$$\frac { 5 } { 6 } [ x - \frac { 1 } { 3 } ] + \frac { 7 } { 6 } [ \frac { x } { 5 } - \frac { 1 } { 7 } ] = 4 \frac { 8 } { 9 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 630, the least common multiple of 6,3,5,7,9.

$$525\left(x-\frac{1}{3}\right)+735\left(\frac{x}{5}-\frac{1}{7}\right)=70\left(4\times 9+8\right)$$

Use the distributive property to multiply 525 by x-\frac{1}{3}.

$$525x+525\left(-\frac{1}{3}\right)+735\left(\frac{x}{5}-\frac{1}{7}\right)=70\left(4\times 9+8\right)$$

Express 525\left(-\frac{1}{3}\right) as a single fraction.

$$525x+\frac{525\left(-1\right)}{3}+735\left(\frac{x}{5}-\frac{1}{7}\right)=70\left(4\times 9+8\right)$$

Multiply 525 and -1 to get -525.

$$525x+\frac{-525}{3}+735\left(\frac{x}{5}-\frac{1}{7}\right)=70\left(4\times 9+8\right)$$

Divide -525 by 3 to get -175.

$$525x-175+735\left(\frac{x}{5}-\frac{1}{7}\right)=70\left(4\times 9+8\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 7 is 35. Multiply \frac{x}{5} times \frac{7}{7}. Multiply \frac{1}{7} times \frac{5}{5}.

$$525x-175+735\left(\frac{7x}{35}-\frac{5}{35}\right)=70\left(4\times 9+8\right)$$

Since \frac{7x}{35} and \frac{5}{35} have the same denominator, subtract them by subtracting their numerators.

$$525x-175+735\times \frac{7x-5}{35}=70\left(4\times 9+8\right)$$

Cancel out 35, the greatest common factor in 735 and 35.

$$525x-175+21\left(7x-5\right)=70\left(4\times 9+8\right)$$

Use the distributive property to multiply 21 by 7x-5.

$$525x-175+147x-105=70\left(4\times 9+8\right)$$

Combine 525x and 147x to get 672x.

$$672x-175-105=70\left(4\times 9+8\right)$$

Subtract 105 from -175 to get -280.

$$672x-280=70\left(4\times 9+8\right)$$

Multiply 4 and 9 to get 36.

$$672x-280=70\left(36+8\right)$$

Add 36 and 8 to get 44.

$$672x-280=70\times 44$$

Multiply 70 and 44 to get 3080.

$$672x-280=3080$$

Add 280 to both sides.

$$672x=3080+280$$

Add 3080 and 280 to get 3360.

$$672x=3360$$

Divide both sides by 672.

$$x=\frac{3360}{672}$$

Divide 3360 by 672 to get 5.

$$x=5$$