Solve (x-4)(6div3600)=(x-67)(48div3600)

$$(x-4)(6 \div 3600)=(x-67)(48 \div 3600)$$

Solve for x

$$x=76$$

Steps for Solving Linear Equation

Reduce the fraction \frac{6}{3600} to lowest terms by extracting and canceling out 6.

$$\left(x-4\right)\times \frac{1}{600}=\left(x-67\right)\times \frac{48}{3600}$$

Use the distributive property to multiply x-4 by \frac{1}{600}.

$$x\times \frac{1}{600}-4\times \frac{1}{600}=\left(x-67\right)\times \frac{48}{3600}$$

Multiply -4 and \frac{1}{600} to get \frac{-4}{600}.

$$x\times \frac{1}{600}+\frac{-4}{600}=\left(x-67\right)\times \frac{48}{3600}$$

Reduce the fraction \frac{-4}{600} to lowest terms by extracting and canceling out 4.

$$x\times \frac{1}{600}-\frac{1}{150}=\left(x-67\right)\times \frac{48}{3600}$$

Reduce the fraction \frac{48}{3600} to lowest terms by extracting and canceling out 48.

$$x\times \frac{1}{600}-\frac{1}{150}=\left(x-67\right)\times \frac{1}{75}$$

Use the distributive property to multiply x-67 by \frac{1}{75}.

$$x\times \frac{1}{600}-\frac{1}{150}=x\times \frac{1}{75}-67\times \frac{1}{75}$$

Multiply -67 and \frac{1}{75} to get \frac{-67}{75}.

$$x\times \frac{1}{600}-\frac{1}{150}=x\times \frac{1}{75}+\frac{-67}{75}$$

Fraction \frac{-67}{75} can be rewritten as -\frac{67}{75} by extracting the negative sign.

$$x\times \frac{1}{600}-\frac{1}{150}=x\times \frac{1}{75}-\frac{67}{75}$$

Subtract x\times \frac{1}{75} from both sides.

$$x\times \frac{1}{600}-\frac{1}{150}-x\times \frac{1}{75}=-\frac{67}{75}$$

Combine x\times \frac{1}{600} and -x\times \frac{1}{75} to get -\frac{7}{600}x.

$$-\frac{7}{600}x-\frac{1}{150}=-\frac{67}{75}$$

Add \frac{1}{150} to both sides.

$$-\frac{7}{600}x=-\frac{67}{75}+\frac{1}{150}$$

Least common multiple of 75 and 150 is 150. Convert -\frac{67}{75} and \frac{1}{150} to fractions with denominator 150.

$$-\frac{7}{600}x=-\frac{134}{150}+\frac{1}{150}$$

Since -\frac{134}{150} and \frac{1}{150} have the same denominator, add them by adding their numerators.

$$-\frac{7}{600}x=\frac{-134+1}{150}$$

Add -134 and 1 to get -133.

$$-\frac{7}{600}x=-\frac{133}{150}$$

Multiply both sides by -\frac{600}{7}, the reciprocal of -\frac{7}{600}.

$$x=-\frac{133}{150}\left(-\frac{600}{7}\right)$$

Multiply -\frac{133}{150} times -\frac{600}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-133\left(-600\right)}{150\times 7}$$

Do the multiplications in the fraction \frac{-133\left(-600\right)}{150\times 7}.

$$x=\frac{79800}{1050}$$

Divide 79800 by 1050 to get 76.

$$x=76$$