Solve 5/3y+1leq-2y-3/4

$$\frac { 5 } { 3 } y + 1 \leq - 2 y - \frac { 3 } { 4 }$$

Solve for y

$$y\leq -\frac{21}{44}$$

Solution Steps

Add 2y to both sides.

$$\frac{5}{3}y+1+2y\leq -\frac{3}{4}$$

Combine \frac{5}{3}y and 2y to get \frac{11}{3}y.

$$\frac{11}{3}y+1\leq -\frac{3}{4}$$

Subtract 1 from both sides.

$$\frac{11}{3}y\leq -\frac{3}{4}-1$$

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

$$\frac{11}{3}y\leq -\frac{3}{4}-\frac{4}{4}$$

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

$$\frac{11}{3}y\leq \frac{-3-4}{4}$$

Subtract 4 from -3 to get -7.

$$\frac{11}{3}y\leq -\frac{7}{4}$$

Multiply both sides by \frac{3}{11}, the reciprocal of \frac{11}{3}. Since \frac{11}{3} is positive, the inequality direction remains the same.

$$y\leq -\frac{7}{4}\times \frac{3}{11}$$

Multiply -\frac{7}{4} times \frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$y\leq \frac{-7\times 3}{4\times 11}$$

Do the multiplications in the fraction \frac{-7\times 3}{4\times 11}.

$$y\leq \frac{-21}{44}$$

Fraction \frac{-21}{44} can be rewritten as -\frac{21}{44} by extracting the negative sign.

$$y\leq -\frac{21}{44}$$