solve the inequality

Question

8x−16>2(3x−12)

Answer 1

8x−16>2(3x−12)

First, use distributive property on the right - a(b-c) = (a*b - a*c). This will yield:

8x - 16 > 6x - 24

Then, group the variable and constant terms separately. To achieve that, subtract 6x from both sides and add 16 to both sides.

2x > -8

Divide both sides by 2 to get x

x > -4

This is the final answer. x can take any value which is greater than -4, that includes -3, -2, -1, 0, 1,2, 3 etc

Hope this helps!

Answer 2

Anytime you solve an equation or inequality you want to make sure you simplify both sides, this means to make sure each side only as one term with the variable and no parenthesis.

In this example we would need to start by distributing 2 into 3x-12 to simplify this means you're multiplying 3x and -12 by 2.

8x-16 > 6x-24

Now we need the variable on one side of the equation. You can move 8x or 6x but I would suggest to keep our variable terms positive so to do this we will subtract 6x from both sides.

8x-16 > 6x-24

-6x -6x

2x-16> -24

Finally we can treat this like any other inequality or equation and get the variable alone. We would start by adding 16 to both sides.

8x-16 > -24

+16 +16

8x > -8

÷8 ÷8

x > -1

Answer 3

8x−16 > 2(3x−12)

Note: The goal is to solve for the inequality by isolating x.

1) Apply the distribution to the left-hand side of the inequality to get 8x -16 > 6x - 24

2) Place the "x" terms on one side to get 2x - 16 > -24

3) Add 16 to both sides of the inequality to get 2x > -8

4) Divide both sides by 2 to get x > -4

Answer 4

8x - 16 > 2 (3x - 12)

First expand the right side using multiplication

8x - 16 > 6x - 24

We subtract 6x in both sides by subtracting them from both sides

8x - 6x - 16 > -24

We simplify 8x - 6x, getting 2x on the left

2x - 16 > -24

We add 16 to both sides, and get

2x > - 8

We divide 2 from both sides, and get

x > -4

Answer 5

8x-16>2(3x-12)

Step 1: Distribute

8x-16>6x-24

Step 2: Combine like terms

(8x-6x)-16>-24

2x-16>-24

There are more like terms

2x>(-24+16)

2x>-8

Step 3: Isolate the variable

x>-4 (Divide on both sides)

x>-4