Solve 4/10x+1=3/4(x-1

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}x+1=\frac{3}{4}\left(x-1\right)$$

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

$$\frac{2}{5}x+1=\frac{3}{4}x+\frac{3}{4}\left(-1\right)$$

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

$$\frac{2}{5}x+1=\frac{3}{4}x-\frac{3}{4}$$

Subtract \frac{3}{4}x from both sides.

$$\frac{2}{5}x+1-\frac{3}{4}x=-\frac{3}{4}$$

Combine \frac{2}{5}x and -\frac{3}{4}x to get -\frac{7}{20}x.

$$-\frac{7}{20}x+1=-\frac{3}{4}$$

Subtract 1 from both sides.

$$-\frac{7}{20}x=-\frac{3}{4}-1$$

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

$$-\frac{7}{20}x=-\frac{3}{4}-\frac{4}{4}$$

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

$$-\frac{7}{20}x=\frac{-3-4}{4}$$

Subtract 4 from -3 to get -7.

$$-\frac{7}{20}x=-\frac{7}{4}$$

Multiply both sides by -\frac{20}{7}, the reciprocal of -\frac{7}{20}.

$$x=-\frac{7}{4}\left(-\frac{20}{7}\right)$$

Multiply -\frac{7}{4} times -\frac{20}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\left(-20\right)}{4\times 7}$$

Do the multiplications in the fraction \frac{-7\left(-20\right)}{4\times 7}.

$$x=\frac{140}{28}$$

Divide 140 by 28 to get 5.

$$x=5$$