Solve 3/4x+2xgeq5/2+2/3

$$\frac { 3 } { 4 } x + 2 x \geq \frac { 5 } { 2 } + \frac { 2 } { 3 }$$

Solve for x

$$x\geq \frac{38}{33}$$

Solution Steps

Combine \frac{3}{4}x and 2x to get \frac{11}{4}x.

$$\frac{11}{4}x\geq \frac{5}{2}+\frac{2}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{11}{4}x\geq \frac{15}{6}+\frac{4}{6}$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{11}{4}x\geq \frac{15+4}{6}$$

Add 15 and 4 to get 19.

$$\frac{11}{4}x\geq \frac{19}{6}$$

Multiply both sides by \frac{4}{11}, the reciprocal of \frac{11}{4}. Since \frac{11}{4} is positive, the inequality direction remains the same.

$$x\geq \frac{19}{6}\times \frac{4}{11}$$

Multiply \frac{19}{6} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{19\times 4}{6\times 11}$$

Do the multiplications in the fraction \frac{19\times 4}{6\times 11}.

$$x\geq \frac{76}{66}$$

Reduce the fraction \frac{76}{66} to lowest terms by extracting and canceling out 2.

$$x\geq \frac{38}{33}$$