How do you do: -2(x+4)< 6x + 16?

Answer 1

1. divide by -2 so you get:
x+4 > -3x - 8
2. subtract 4 from both sides
x > -3x -12
3. add -3x to both sides
4x > -12
4. divide by 4 on both sides
x > -3

Answer 2

I prefer to just put in a few x values

If x = 0, -2(4) < 0 + 16

-8 < 16 which is true.

If x = 10, then -2 * 14 < 76 obviously

now if x = -10, -2 * -6 >-60 + 16 since
12> -44

so now we can see that if we solve the equation, we know more or less what the answer should be:

-2x -8 < 6x + 16

If we just solve it just like an equation, then we will find the answer or it will be the opposite of our number.
so 24 < 8 x 3 < x so x is 3 or -3

We plug in -3 and it works.

-2 ( -3 +4) < 6 * -3 + 16

-2 * 1 < -18 + 16

-2 = -2 it works!!!

Answer 3

Temporarily change the < to = and solve the equation.

-2x -8 = 6x +16
-2x +2x -8 = 6x +2x +16
-8-16 = 8x +16 -16
-24 = 8x
-3 = x


Then substitute the original inequality, resulting in:

-3 < x

Therefore, x > -3 is the solution set

Answer 4

Use distributive property:
-2x-8<6x+16

Subtract 6x from both side:
-8x-8<16

Add 8 from both sides:
-8x<24

Divide -8 from both sides:
x>-3
The sign changed from less than to greater than because you divided both sides by a negative number.

Check:
-2(-3+4)=6(-3)+16
-2(1)=-18+16
-2=-2

I hope this helps!

Answer 5

distribute the -2
-2x -8 < 6x + 16
add 2x to both sides
-2x + 2x -8 < 6x + 16 + 2x
-8 < 8x + 16
subtract 16 from both sides
-16 -8 < 8x + 16-16
-24 < 8x
divide both sides by 8
-24/8 < 8x/8
-3 < x
x > -3