Solve 75%(x-1)-25%(x-4)=25%(x+6)

$$75 \% ( x - 1 ) - 25 \% ( x - 4 ) = 25 \% ( x + 6 )$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{3}{4}\left(x-1\right)-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

Use the distributive property to multiply \frac{3}{4} by x-1.

$$\frac{3}{4}x+\frac{3}{4}\left(-1\right)-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

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

$$\frac{3}{4}x-\frac{3}{4}-\frac{25}{100}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}\left(x-4\right)=\frac{25}{100}\left(x+6\right)$$

Use the distributive property to multiply -\frac{1}{4} by x-4.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x-\frac{1}{4}\left(-4\right)=\frac{25}{100}\left(x+6\right)$$

Express -\frac{1}{4}\left(-4\right) as a single fraction.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+\frac{-\left(-4\right)}{4}=\frac{25}{100}\left(x+6\right)$$

Multiply -1 and -4 to get 4.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+\frac{4}{4}=\frac{25}{100}\left(x+6\right)$$

Divide 4 by 4 to get 1.

$$\frac{3}{4}x-\frac{3}{4}-\frac{1}{4}x+1=\frac{25}{100}\left(x+6\right)$$

Combine \frac{3}{4}x and -\frac{1}{4}x to get \frac{1}{2}x.

$$\frac{1}{2}x-\frac{3}{4}+1=\frac{25}{100}\left(x+6\right)$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{2}x-\frac{3}{4}+\frac{4}{4}=\frac{25}{100}\left(x+6\right)$$

Since -\frac{3}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x+\frac{-3+4}{4}=\frac{25}{100}\left(x+6\right)$$

Add -3 and 4 to get 1.

$$\frac{1}{2}x+\frac{1}{4}=\frac{25}{100}\left(x+6\right)$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}\left(x+6\right)$$

Use the distributive property to multiply \frac{1}{4} by x+6.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}x+\frac{1}{4}\times 6$$

Multiply \frac{1}{4} and 6 to get \frac{6}{4}.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}x+\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x+\frac{1}{4}=\frac{1}{4}x+\frac{3}{2}$$

Subtract \frac{1}{4}x from both sides.

$$\frac{1}{2}x+\frac{1}{4}-\frac{1}{4}x=\frac{3}{2}$$

Combine \frac{1}{2}x and -\frac{1}{4}x to get \frac{1}{4}x.

$$\frac{1}{4}x+\frac{1}{4}=\frac{3}{2}$$

Subtract \frac{1}{4} from both sides.

$$\frac{1}{4}x=\frac{3}{2}-\frac{1}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{1}{4}x=\frac{6}{4}-\frac{1}{4}$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}x=\frac{6-1}{4}$$

Subtract 1 from 6 to get 5.

$$\frac{1}{4}x=\frac{5}{4}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x=\frac{5}{4}\times 4$$

Cancel out 4 and 4.

$$x=5$$