Solve 2x+4geq1/2x-2/3

$$2 x + 4 \geq \frac { 1 } { 2 } x - \frac { 2 } { 3 }$$

Solve for x

$$x\geq -\frac{28}{9}$$

Solution Steps

Subtract \frac{1}{2}x from both sides.

$$2x+4-\frac{1}{2}x\geq -\frac{2}{3}$$

Combine 2x and -\frac{1}{2}x to get \frac{3}{2}x.

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

Subtract 4 from both sides.

$$\frac{3}{2}x\geq -\frac{2}{3}-4$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{3}{2}x\geq -\frac{2}{3}-\frac{12}{3}$$

Since -\frac{2}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}x\geq \frac{-2-12}{3}$$

Subtract 12 from -2 to get -14.

$$\frac{3}{2}x\geq -\frac{14}{3}$$

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

$$x\geq -\frac{14}{3}\times \frac{2}{3}$$

Multiply -\frac{14}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{-14\times 2}{3\times 3}$$

Do the multiplications in the fraction \frac{-14\times 2}{3\times 3}.

$$x\geq \frac{-28}{9}$$

Fraction \frac{-28}{9} can be rewritten as -\frac{28}{9} by extracting the negative sign.

$$x\geq -\frac{28}{9}$$