Solve 2/3x-5/4<4/7x+1

$$\frac { 2 } { 3 } x - \frac { 5 } { 4 } < \frac { 4 } { 7 } x + 1$$

Solve for x

$$x<\frac{189}{8}$$

Solution Steps

Subtract \frac{4}{7}x from both sides.

$$\frac{2}{3}x-\frac{5}{4}-\frac{4}{7}x<1$$

Combine \frac{2}{3}x and -\frac{4}{7}x to get \frac{2}{21}x.

$$\frac{2}{21}x-\frac{5}{4}<1$$

Add \frac{5}{4} to both sides.

$$\frac{2}{21}x<1+\frac{5}{4}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{2}{21}x<\frac{4}{4}+\frac{5}{4}$$

Since \frac{4}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{21}x<\frac{4+5}{4}$$

Add 4 and 5 to get 9.

$$\frac{2}{21}x<\frac{9}{4}$$

Multiply both sides by \frac{21}{2}, the reciprocal of \frac{2}{21}. Since \frac{2}{21} is positive, the inequality direction remains the same.

$$x<\frac{9}{4}\times \frac{21}{2}$$

Multiply \frac{9}{4} times \frac{21}{2} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{9\times 21}{4\times 2}$$

Do the multiplications in the fraction \frac{9\times 21}{4\times 2}.

$$x<\frac{189}{8}$$