Solve 5(24v-1*4)geq-6(0.8+12v)

$$5 ( 24 v - 1 \cdot 4 ) \geq - 6 ( 0.8 + 12 v )$$

Solve for v

$$v\geq \frac{19}{240}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$5\left(24v-4\right)\geq -6\left(0.8+12v\right)$$

Use the distributive property to multiply 5 by 24v-4.

$$120v-20\geq -6\left(0.8+12v\right)$$

Use the distributive property to multiply -6 by 0.8+12v.

$$120v-20\geq -4.8-72v$$

Add 72v to both sides.

$$120v-20+72v\geq -4.8$$

Combine 120v and 72v to get 192v.

$$192v-20\geq -4.8$$

Add 20 to both sides.

$$192v\geq -4.8+20$$

Add -4.8 and 20 to get 15.2.

$$192v\geq 15.2$$

Divide both sides by 192. Since 192 is positive, the inequality direction remains the same.

$$v\geq \frac{15.2}{192}$$

Expand \frac{15.2}{192} by multiplying both numerator and the denominator by 10.

$$v\geq \frac{152}{1920}$$

Reduce the fraction \frac{152}{1920} to lowest terms by extracting and canceling out 8.

$$v\geq \frac{19}{240}$$