Solve 4x-3(-7/5x+53/5)=31

$$4 x - 3 ( \frac { - 7 } { 5 } x + \frac { 53 } { 5 } ) = 31$$

Solve for x

$$x = \frac{314}{41} = 7\frac{27}{41} \approx 7.658536585$$

Steps for Solving Linear Equation

Fraction \frac{-7}{5} can be rewritten as -\frac{7}{5} by extracting the negative sign.

$$4x-3\left(-\frac{7}{5}x+\frac{53}{5}\right)=31$$

Use the distributive property to multiply -3 by -\frac{7}{5}x+\frac{53}{5}.

$$4x-3\left(-\frac{7}{5}\right)x-3\times \frac{53}{5}=31$$

Express -3\left(-\frac{7}{5}\right) as a single fraction.

$$4x+\frac{-3\left(-7\right)}{5}x-3\times \frac{53}{5}=31$$

Multiply -3 and -7 to get 21.

$$4x+\frac{21}{5}x-3\times \frac{53}{5}=31$$

Express -3\times \frac{53}{5} as a single fraction.

$$4x+\frac{21}{5}x+\frac{-3\times 53}{5}=31$$

Multiply -3 and 53 to get -159.

$$4x+\frac{21}{5}x+\frac{-159}{5}=31$$

Fraction \frac{-159}{5} can be rewritten as -\frac{159}{5} by extracting the negative sign.

$$4x+\frac{21}{5}x-\frac{159}{5}=31$$

Combine 4x and \frac{21}{5}x to get \frac{41}{5}x.

$$\frac{41}{5}x-\frac{159}{5}=31$$

Add \frac{159}{5} to both sides.

$$\frac{41}{5}x=31+\frac{159}{5}$$

Convert 31 to fraction \frac{155}{5}.

$$\frac{41}{5}x=\frac{155}{5}+\frac{159}{5}$$

Since \frac{155}{5} and \frac{159}{5} have the same denominator, add them by adding their numerators.

$$\frac{41}{5}x=\frac{155+159}{5}$$

Add 155 and 159 to get 314.

$$\frac{41}{5}x=\frac{314}{5}$$

Multiply both sides by \frac{5}{41}, the reciprocal of \frac{41}{5}.

$$x=\frac{314}{5}\times \frac{5}{41}$$

Multiply \frac{314}{5} times \frac{5}{41} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{314\times 5}{5\times 41}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{314}{41}$$