Solve 2/3(x+4)leq1/2

$$\frac { 2 } { 3 } ( x + 4 ) \leq \frac { 1 } { 2 }$$

Solve for x

$$x\leq -\frac{13}{4}$$

Solution Steps

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}. Since \frac{2}{3} is positive, the inequality direction remains the same.

$$x+4\leq \frac{1}{2}\times \frac{3}{2}$$

Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x+4\leq \frac{1\times 3}{2\times 2}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.

$$x+4\leq \frac{3}{4}$$

Subtract 4 from both sides.

$$x\leq \frac{3}{4}-4$$

Convert 4 to fraction \frac{16}{4}.

$$x\leq \frac{3}{4}-\frac{16}{4}$$

Since \frac{3}{4} and \frac{16}{4} have the same denominator, subtract them by subtracting their numerators.

$$x\leq \frac{3-16}{4}$$

Subtract 16 from 3 to get -13.

$$x\leq -\frac{13}{4}$$