Question

-3v - 14> 3v+16 It’s for my final review and I’m so confused

Answer 1

v < -5

Explanation:

Add 14 to each side

`-3v-14+14 > 3v+16+14`

Next, you need to simplify these additions by adding non-variable integers

`16 + 14 = 30\\= 3v + 30\\= -3v > 3v + 30`

Now, subtract each side by 3v, the leading term in this equation.

`-3v-3v > 3v+30-3v`

Again, we must simplify to get to the next step. This time we are dealing with a negative minus a negative. There on, things get trickier. In short words, a negative minus a positive is going to have a negative result, because both sides are treated as a negative plus a negative. In an equation, -a - b is the same as -a + -b.

`-3v - 3v = -3v + -3v\\= -6v\\3v + -3v = 3v - 3v\\= 0\\= 0 + 30\\= 30\\= -6v > 30`

Next, we must multiply both sides by -1. The reason we're multiplying by a negative instead of a positive is because we are reversing the inequality.

`= -6v* -1 < 30* 1`

Notice the change from greater than to less than.

IMPORTANT NOTE: A negative times a negative is a positive, a positive times a positive is also a positive. Lastly, a negative times a positive is a negative.

`-6v* -1 = 6v\\30* -1 = -30\\= 6v < -30`

For the next step, we must divide by 6, because 6 can be divided by 6, and -30 can also be divided by 6 fairly.

`(6v)/(6) < (-30)/(6)\\(6v)/(6) = (6* v)/(6)\\Assume\:v=1!\\= (6* 1)/(6)\\= (6)/(6)\\= 1\\= v`

`(-30)/(6)\\\\(-a)/b = (-a/b)\\\\=-(30)/(6)\\= -5`

And therefore, v is less than -5.

If you need anything else, let me know!

Hope this helps!

Answer 2

The given inequality is

-3v - 14 > 3v + 16,

Add 3v on both side of the inequality

-3v -14 +3v > 3v +16 +3v

-3v +3v -14 > 3v + 3v + 16

0 - 14 > 6v + 16

Subtract 16 from both side of the equation,

-14 - 16 > 6v + 16 - 16

-30 > 6v + 0

Now subtract 6v from both side,

-30- 6v > 6v - 6v

-6v -30 > 0

Add 30 on both side,

-6v -30 + 30 > 30

-6v > 30

Divide both side by 6:

-6v/6 > 30/6

-v > 5

Multiply both side by (-1)

(-1) (-v) < (-1) 5

v < -5

Thus, v < -5

Answer : v < -5