Solve 0.4(x+3)=1.5x-2/3(x-7)

$$0.4(x+3)=1.5x- \frac{ 2 }{ 3 } (x-7)$$

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.4 by x+3.

$$0.4x+1.2=1.5x-\frac{2}{3}\left(x-7\right)$$

Use the distributive property to multiply -\frac{2}{3} by x-7.

$$0.4x+1.2=1.5x-\frac{2}{3}x-\frac{2}{3}\left(-7\right)$$

Express -\frac{2}{3}\left(-7\right) as a single fraction.

$$0.4x+1.2=1.5x-\frac{2}{3}x+\frac{-2\left(-7\right)}{3}$$

Multiply -2 and -7 to get 14.

$$0.4x+1.2=1.5x-\frac{2}{3}x+\frac{14}{3}$$

Combine 1.5x and -\frac{2}{3}x to get \frac{5}{6}x.

$$0.4x+1.2=\frac{5}{6}x+\frac{14}{3}$$

Subtract \frac{5}{6}x from both sides.

$$0.4x+1.2-\frac{5}{6}x=\frac{14}{3}$$

Combine 0.4x and -\frac{5}{6}x to get -\frac{13}{30}x.

$$-\frac{13}{30}x+1.2=\frac{14}{3}$$

Subtract 1.2 from both sides.

$$-\frac{13}{30}x=\frac{14}{3}-1.2$$

Convert decimal number 1.2 to fraction \frac{12}{10}. Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{30}x=\frac{14}{3}-\frac{6}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{14}{3} and \frac{6}{5} to fractions with denominator 15.

$$-\frac{13}{30}x=\frac{70}{15}-\frac{18}{15}$$

Since \frac{70}{15} and \frac{18}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{30}x=\frac{70-18}{15}$$

Subtract 18 from 70 to get 52.

$$-\frac{13}{30}x=\frac{52}{15}$$

Multiply both sides by -\frac{30}{13}, the reciprocal of -\frac{13}{30}.

$$x=\frac{52}{15}\left(-\frac{30}{13}\right)$$

Multiply \frac{52}{15} times -\frac{30}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{52\left(-30\right)}{15\times 13}$$

Do the multiplications in the fraction \frac{52\left(-30\right)}{15\times 13}.

$$x=\frac{-1560}{195}$$

Divide -1560 by 195 to get -8.

$$x=-8$$