Solve 2/7x+2geq-4x+8/3

$$\frac{ 2 }{ 7 } x+2 \geq -4x+ \frac{ 8 }{ 3 }$$

Solve for x

$$x\geq \frac{7}{45}$$

Solution Steps

Add 4x to both sides.

$$\frac{2}{7}x+2+4x\geq \frac{8}{3}$$

Combine \frac{2}{7}x and 4x to get \frac{30}{7}x.

$$\frac{30}{7}x+2\geq \frac{8}{3}$$

Subtract 2 from both sides.

$$\frac{30}{7}x\geq \frac{8}{3}-2$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{30}{7}x\geq \frac{8}{3}-\frac{6}{3}$$

Since \frac{8}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30}{7}x\geq \frac{8-6}{3}$$

Subtract 6 from 8 to get 2.

$$\frac{30}{7}x\geq \frac{2}{3}$$

Multiply both sides by \frac{7}{30}, the reciprocal of \frac{30}{7}. Since \frac{30}{7} is positive, the inequality direction remains the same.

$$x\geq \frac{2}{3}\times \frac{7}{30}$$

Multiply \frac{2}{3} times \frac{7}{30} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{2\times 7}{3\times 30}$$

Do the multiplications in the fraction \frac{2\times 7}{3\times 30}.

$$x\geq \frac{14}{90}$$

Reduce the fraction \frac{14}{90} to lowest terms by extracting and canceling out 2.

$$x\geq \frac{7}{45}$$