Solve -5left(2.4v-1*4right)geq-6left(0.8+1.2vright)

$$-5 \left( 2.4v-1 \cdot 4 \right) \geq -6 \left( 0.8+1.2v \right)$$

Solve for v

$$v\leq \frac{31}{6}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$-5\left(2.4v-4\right)\geq -6\left(0.8+1.2v\right)$$

Use the distributive property to multiply -5 by 2.4v-4.

$$-12v+20\geq -6\left(0.8+1.2v\right)$$

Use the distributive property to multiply -6 by 0.8+1.2v.

$$-12v+20\geq -4.8-7.2v$$

Add 7.2v to both sides.

$$-12v+20+7.2v\geq -4.8$$

Combine -12v and 7.2v to get -4.8v.

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

Subtract 20 from both sides.

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

Subtract 20 from -4.8 to get -24.8.

$$-4.8v\geq -24.8$$

Divide both sides by -4.8. Since -4.8 is negative, the inequality direction is changed.

$$v\leq \frac{-24.8}{-4.8}$$

Expand \frac{-24.8}{-4.8} by multiplying both numerator and the denominator by 10.

$$v\leq \frac{-248}{-48}$$

Reduce the fraction \frac{-248}{-48} to lowest terms by extracting and canceling out -8.

$$v\leq \frac{31}{6}$$