Solve 4x+10(5/3x+7/3)=6

$$4x+10( \frac{ 5 }{ 3 } x+ \frac{ 7 }{ 3 } )=6$$

Solve for x

$$x=-\frac{26}{31}\approx -0.838709677$$

Steps for Solving Linear Equation

Use the distributive property to multiply 10 by \frac{5}{3}x+\frac{7}{3}.

$$4x+10\times \frac{5}{3}x+10\times \frac{7}{3}=6$$

Express 10\times \frac{5}{3} as a single fraction.

$$4x+\frac{10\times 5}{3}x+10\times \frac{7}{3}=6$$

Multiply 10 and 5 to get 50.

$$4x+\frac{50}{3}x+10\times \frac{7}{3}=6$$

Express 10\times \frac{7}{3} as a single fraction.

$$4x+\frac{50}{3}x+\frac{10\times 7}{3}=6$$

Multiply 10 and 7 to get 70.

$$4x+\frac{50}{3}x+\frac{70}{3}=6$$

Combine 4x and \frac{50}{3}x to get \frac{62}{3}x.

$$\frac{62}{3}x+\frac{70}{3}=6$$

Subtract \frac{70}{3} from both sides.

$$\frac{62}{3}x=6-\frac{70}{3}$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{62}{3}x=\frac{18}{3}-\frac{70}{3}$$

Since \frac{18}{3} and \frac{70}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{62}{3}x=\frac{18-70}{3}$$

Subtract 70 from 18 to get -52.

$$\frac{62}{3}x=-\frac{52}{3}$$

Multiply both sides by \frac{3}{62}, the reciprocal of \frac{62}{3}.

$$x=-\frac{52}{3}\times \frac{3}{62}$$

Multiply -\frac{52}{3} times \frac{3}{62} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-52\times 3}{3\times 62}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{-52}{62}$$

Reduce the fraction \frac{-52}{62} to lowest terms by extracting and canceling out 2.

$$x=-\frac{26}{31}$$