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

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

Solve for x

$$x=\frac{47}{92}\approx 0.510869565$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 2 and -4 to get -8.

$$\frac{2}{3}x+\frac{-8}{3}=\frac{5}{4}-7x$$

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

$$\frac{2}{3}x-\frac{8}{3}=\frac{5}{4}-7x$$

Add 7x to both sides.

$$\frac{2}{3}x-\frac{8}{3}+7x=\frac{5}{4}$$

Combine \frac{2}{3}x and 7x to get \frac{23}{3}x.

$$\frac{23}{3}x-\frac{8}{3}=\frac{5}{4}$$

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

$$\frac{23}{3}x=\frac{5}{4}+\frac{8}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{8}{3} to fractions with denominator 12.

$$\frac{23}{3}x=\frac{15}{12}+\frac{32}{12}$$

Since \frac{15}{12} and \frac{32}{12} have the same denominator, add them by adding their numerators.

$$\frac{23}{3}x=\frac{15+32}{12}$$

Add 15 and 32 to get 47.

$$\frac{23}{3}x=\frac{47}{12}$$

Multiply both sides by \frac{3}{23}, the reciprocal of \frac{23}{3}.

$$x=\frac{47}{12}\times \frac{3}{23}$$

Multiply \frac{47}{12} times \frac{3}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{47\times 3}{12\times 23}$$

Do the multiplications in the fraction \frac{47\times 3}{12\times 23}.

$$x=\frac{141}{276}$$

Reduce the fraction \frac{141}{276} to lowest terms by extracting and canceling out 3.

$$x=\frac{47}{92}$$