Solve 4/7(3w+4)geq4

$$\frac { 4 } { 7 } ( 3 w + 4 ) \geq 4$$

Solve for w

$$w\geq 1$$

Solution Steps

Multiply both sides by \frac{7}{4}, the reciprocal of \frac{4}{7}. Since \frac{4}{7} is positive, the inequality direction remains the same.

$$3w+4\geq 4\times \frac{7}{4}$$

Cancel out 4 and 4.

$$3w+4\geq 7$$

Subtract 4 from both sides.

$$3w\geq 7-4$$

Subtract 4 from 7 to get 3.

$$3w\geq 3$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$w\geq \frac{3}{3}$$

Divide 3 by 3 to get 1.

$$w\geq 1$$