Solve 4/9w+1geq-2w-1/2

$$\frac { 4 } { 9 } w + 1 \geq - 2 w - \frac { 1 } { 2 }$$

Solve for w

$$w\geq -\frac{27}{44}$$

Solution Steps

Add 2w to both sides.

$$\frac{4}{9}w+1+2w\geq -\frac{1}{2}$$

Combine \frac{4}{9}w and 2w to get \frac{22}{9}w.

$$\frac{22}{9}w+1\geq -\frac{1}{2}$$

Subtract 1 from both sides.

$$\frac{22}{9}w\geq -\frac{1}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{22}{9}w\geq -\frac{1}{2}-\frac{2}{2}$$

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22}{9}w\geq \frac{-1-2}{2}$$

Subtract 2 from -1 to get -3.

$$\frac{22}{9}w\geq -\frac{3}{2}$$

Multiply both sides by \frac{9}{22}, the reciprocal of \frac{22}{9}. Since \frac{22}{9} is positive, the inequality direction remains the same.

$$w\geq -\frac{3}{2}\times \frac{9}{22}$$

Multiply -\frac{3}{2} times \frac{9}{22} by multiplying numerator times numerator and denominator times denominator.

$$w\geq \frac{-3\times 9}{2\times 22}$$

Do the multiplications in the fraction \frac{-3\times 9}{2\times 22}.

$$w\geq \frac{-27}{44}$$

Fraction \frac{-27}{44} can be rewritten as -\frac{27}{44} by extracting the negative sign.

$$w\geq -\frac{27}{44}$$