Solve 3/3(6-x)<1/4(x+3)

$$\frac { 3 } { 3 } ( 6 - x ) < \frac { 1 } { 4 } ( x + 3 )$$

Solve for x

$$x>\frac{21}{5}$$

Solution Steps

Divide 3 by 3 to get 1.

$$1\left(6-x\right)<\frac{1}{4}\left(x+3\right)$$

Use the distributive property to multiply 1 by 6-x.

$$6-x<\frac{1}{4}\left(x+3\right)$$

Use the distributive property to multiply \frac{1}{4} by x+3.

$$6-x<\frac{1}{4}x+\frac{1}{4}\times 3$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$6-x<\frac{1}{4}x+\frac{3}{4}$$

Subtract \frac{1}{4}x from both sides.

$$6-x-\frac{1}{4}x<\frac{3}{4}$$

Combine -x and -\frac{1}{4}x to get -\frac{5}{4}x.

$$6-\frac{5}{4}x<\frac{3}{4}$$

Subtract 6 from both sides.

$$-\frac{5}{4}x<\frac{3}{4}-6$$

Convert 6 to fraction \frac{24}{4}.

$$-\frac{5}{4}x<\frac{3}{4}-\frac{24}{4}$$

Since \frac{3}{4} and \frac{24}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{4}x<\frac{3-24}{4}$$

Subtract 24 from 3 to get -21.

$$-\frac{5}{4}x<-\frac{21}{4}$$

Multiply both sides by -\frac{4}{5}, the reciprocal of -\frac{5}{4}. Since -\frac{5}{4} is negative, the inequality direction is changed.

$$x>-\frac{21}{4}\left(-\frac{4}{5}\right)$$

Multiply -\frac{21}{4} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-21\left(-4\right)}{4\times 5}$$

Do the multiplications in the fraction \frac{-21\left(-4\right)}{4\times 5}.

$$x>\frac{84}{20}$$

Reduce the fraction \frac{84}{20} to lowest terms by extracting and canceling out 4.

$$x>\frac{21}{5}$$