Solve 3.1v-1.4geq1.3v+6.7

$$3.1 v - 1.4 \geq 1.3 v + 6.7$$

Solve for v

$$v\geq 4.5$$

Solution Steps

Subtract 1.3v from both sides.

$$3.1v-1.4-1.3v\geq 6.7$$

Combine 3.1v and -1.3v to get 1.8v.

$$1.8v-1.4\geq 6.7$$

Add 1.4 to both sides.

$$1.8v\geq 6.7+1.4$$

Add 6.7 and 1.4 to get 8.1.

$$1.8v\geq 8.1$$

Divide both sides by 1.8. Since 1.8 is positive, the inequality direction remains the same.

$$v\geq \frac{8.1}{1.8}$$

Expand \frac{8.1}{1.8} by multiplying both numerator and the denominator by 10.

$$v\geq \frac{81}{18}$$

Reduce the fraction \frac{81}{18} to lowest terms by extracting and canceling out 9.

$$v\geq \frac{9}{2}$$