Solve 4/3(5x-2)=7[x-(5x-2)]

$$\frac { 4 } { 3 } ( 5 x - 2 ) = 7 [ x - ( 5 x - 2 ) ]$$

Solve for x

$$x=\frac{25}{52}\approx 0.480769231$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{3} by 5x-2.

$$\frac{4}{3}\times 5x+\frac{4}{3}\left(-2\right)=7\left(x-\left(5x-2\right)\right)$$

Express \frac{4}{3}\times 5 as a single fraction.

$$\frac{4\times 5}{3}x+\frac{4}{3}\left(-2\right)=7\left(x-\left(5x-2\right)\right)$$

Multiply 4 and 5 to get 20.

$$\frac{20}{3}x+\frac{4}{3}\left(-2\right)=7\left(x-\left(5x-2\right)\right)$$

Express \frac{4}{3}\left(-2\right) as a single fraction.

$$\frac{20}{3}x+\frac{4\left(-2\right)}{3}=7\left(x-\left(5x-2\right)\right)$$

Multiply 4 and -2 to get -8.

$$\frac{20}{3}x+\frac{-8}{3}=7\left(x-\left(5x-2\right)\right)$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{20}{3}x-\frac{8}{3}=7\left(x-\left(5x-2\right)\right)$$

To find the opposite of 5x-2, find the opposite of each term.

$$\frac{20}{3}x-\frac{8}{3}=7\left(x-5x-\left(-2\right)\right)$$

The opposite of -2 is 2.

$$\frac{20}{3}x-\frac{8}{3}=7\left(x-5x+2\right)$$

Combine x and -5x to get -4x.

$$\frac{20}{3}x-\frac{8}{3}=7\left(-4x+2\right)$$

Use the distributive property to multiply 7 by -4x+2.

$$\frac{20}{3}x-\frac{8}{3}=-28x+14$$

Add 28x to both sides.

$$\frac{20}{3}x-\frac{8}{3}+28x=14$$

Combine \frac{20}{3}x and 28x to get \frac{104}{3}x.

$$\frac{104}{3}x-\frac{8}{3}=14$$

Add \frac{8}{3} to both sides.

$$\frac{104}{3}x=14+\frac{8}{3}$$

Convert 14 to fraction \frac{42}{3}.

$$\frac{104}{3}x=\frac{42}{3}+\frac{8}{3}$$

Since \frac{42}{3} and \frac{8}{3} have the same denominator, add them by adding their numerators.

$$\frac{104}{3}x=\frac{42+8}{3}$$

Add 42 and 8 to get 50.

$$\frac{104}{3}x=\frac{50}{3}$$

Multiply both sides by \frac{3}{104}, the reciprocal of \frac{104}{3}.

$$x=\frac{50}{3}\times \frac{3}{104}$$

Multiply \frac{50}{3} times \frac{3}{104} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{50\times 3}{3\times 104}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{50}{104}$$

Reduce the fraction \frac{50}{104} to lowest terms by extracting and canceling out 2.

$$x=\frac{25}{52}$$