Solve 4/5f-1/2geq21/10

$$\frac { 4 } { 5 } f - \frac { 1 } { 2 } \geq 2 \frac { 1 } { 10 }$$

Solve for f

$$f\geq \frac{13}{4}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2,10. Since 10 is positive, the inequality direction remains the same.

$$8f-5\geq 2\times 10+1$$

Multiply 2 and 10 to get 20.

$$8f-5\geq 20+1$$

Add 20 and 1 to get 21.

$$8f-5\geq 21$$

Add 5 to both sides.

$$8f\geq 21+5$$

Add 21 and 5 to get 26.

$$8f\geq 26$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$f\geq \frac{26}{8}$$

Reduce the fraction \frac{26}{8} to lowest terms by extracting and canceling out 2.

$$f\geq \frac{13}{4}$$