Solve 1-1/3(x-7)=4(x-10)

$$1- \frac{ 1 }{ 3 } (x-7)=4(x-10)$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{3} by x-7.

$$1-\frac{1}{3}x-\frac{1}{3}\left(-7\right)=4\left(x-10\right)$$

Express -\frac{1}{3}\left(-7\right) as a single fraction.

$$1-\frac{1}{3}x+\frac{-\left(-7\right)}{3}=4\left(x-10\right)$$

Multiply -1 and -7 to get 7.

$$1-\frac{1}{3}x+\frac{7}{3}=4\left(x-10\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}-\frac{1}{3}x+\frac{7}{3}=4\left(x-10\right)$$

Since \frac{3}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+7}{3}-\frac{1}{3}x=4\left(x-10\right)$$

Add 3 and 7 to get 10.

$$\frac{10}{3}-\frac{1}{3}x=4\left(x-10\right)$$

Use the distributive property to multiply 4 by x-10.

$$\frac{10}{3}-\frac{1}{3}x=4x-40$$

Subtract 4x from both sides.

$$\frac{10}{3}-\frac{1}{3}x-4x=-40$$

Combine -\frac{1}{3}x and -4x to get -\frac{13}{3}x.

$$\frac{10}{3}-\frac{13}{3}x=-40$$

Subtract \frac{10}{3} from both sides.

$$-\frac{13}{3}x=-40-\frac{10}{3}$$

Convert -40 to fraction -\frac{120}{3}.

$$-\frac{13}{3}x=-\frac{120}{3}-\frac{10}{3}$$

Since -\frac{120}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{3}x=\frac{-120-10}{3}$$

Subtract 10 from -120 to get -130.

$$-\frac{13}{3}x=-\frac{130}{3}$$

Multiply both sides by -\frac{3}{13}, the reciprocal of -\frac{13}{3}.

$$x=-\frac{130}{3}\left(-\frac{3}{13}\right)$$

Multiply -\frac{130}{3} times -\frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-130\left(-3\right)}{3\times 13}$$

Do the multiplications in the fraction \frac{-130\left(-3\right)}{3\times 13}.

$$x=\frac{390}{39}$$

Divide 390 by 39 to get 10.

$$x=10$$