Solve 1/8left(x+7right)=1/7left(x-4right)+1

$$\frac{ 1 }{ 8 } \left( x+7 \right) = \frac{ 1 }{ 7 } \left( x-4 \right) +1$$

Solve for x

$$x=25$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{8} by x+7.

$$\frac{1}{8}x+\frac{1}{8}\times 7=\frac{1}{7}\left(x-4\right)+1$$

Multiply \frac{1}{8} and 7 to get \frac{7}{8}.

$$\frac{1}{8}x+\frac{7}{8}=\frac{1}{7}\left(x-4\right)+1$$

Use the distributive property to multiply \frac{1}{7} by x-4.

$$\frac{1}{8}x+\frac{7}{8}=\frac{1}{7}x+\frac{1}{7}\left(-4\right)+1$$

Multiply \frac{1}{7} and -4 to get \frac{-4}{7}.

$$\frac{1}{8}x+\frac{7}{8}=\frac{1}{7}x+\frac{-4}{7}+1$$

Fraction \frac{-4}{7} can be rewritten as -\frac{4}{7} by extracting the negative sign.

$$\frac{1}{8}x+\frac{7}{8}=\frac{1}{7}x-\frac{4}{7}+1$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{1}{8}x+\frac{7}{8}=\frac{1}{7}x-\frac{4}{7}+\frac{7}{7}$$

Since -\frac{4}{7} and \frac{7}{7} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}x+\frac{7}{8}=\frac{1}{7}x+\frac{-4+7}{7}$$

Add -4 and 7 to get 3.

$$\frac{1}{8}x+\frac{7}{8}=\frac{1}{7}x+\frac{3}{7}$$

Subtract \frac{1}{7}x from both sides.

$$\frac{1}{8}x+\frac{7}{8}-\frac{1}{7}x=\frac{3}{7}$$

Combine \frac{1}{8}x and -\frac{1}{7}x to get -\frac{1}{56}x.

$$-\frac{1}{56}x+\frac{7}{8}=\frac{3}{7}$$

Subtract \frac{7}{8} from both sides.

$$-\frac{1}{56}x=\frac{3}{7}-\frac{7}{8}$$

Least common multiple of 7 and 8 is 56. Convert \frac{3}{7} and \frac{7}{8} to fractions with denominator 56.

$$-\frac{1}{56}x=\frac{24}{56}-\frac{49}{56}$$

Since \frac{24}{56} and \frac{49}{56} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{56}x=\frac{24-49}{56}$$

Subtract 49 from 24 to get -25.

$$-\frac{1}{56}x=-\frac{25}{56}$$

Multiply both sides by -56, the reciprocal of -\frac{1}{56}.

$$x=-\frac{25}{56}\left(-56\right)$$

Express -\frac{25}{56}\left(-56\right) as a single fraction.

$$x=\frac{-25\left(-56\right)}{56}$$

Multiply -25 and -56 to get 1400.

$$x=\frac{1400}{56}$$

Divide 1400 by 56 to get 25.

$$x=25$$