Question

2(2x-8)-8x < 0

Answer 1

5x+(x-8)>9/2(2x-4)

Answer 2

To solve the inequality \( 2(2x - 8) - 8x < 0 \), let's first simplify the expression:

1. Distribute the \( 2 \) in the first term:
\[
2(2x) - 2(8) - 8x < 0
\]
This becomes:
\[
4x - 16 - 8x < 0
\]

2. Combine like terms:
\[
4x - 8x - 16 < 0
\]
Simplifying this gives:
\[
-4x - 16 < 0
\]

3. Add \( 16 \) to both sides:
\[
-4x < 16
\]

4. Divide both sides by \( -4 \). Remember, when you divide by a negative number, you need to reverse the inequality sign:
\[
x > -4
\]

So, the solution to the inequality \( 2(2x - 8) - 8x < 0 \) is:
\[
x > -4
\]

In interval notation, the solution is:
\[
(-4, \infty)
\]

Answer 3

To solve the inequality \( 5x + (x - 8) > \frac{9}{2}(2x - 4) \), let's simplify it step by step.

### Step 1: Expand both sides

First, simplify the left side:
\[
5x + (x - 8) = 5x + x - 8 = 6x - 8
\]

Now simplify the right side:
\[
\frac{9}{2}(2x - 4) = \frac{9}{2} \cdot 2x - \frac{9}{2} \cdot 4 = 9x - 18
\]

### Step 2: Set up the inequality

Now substitute these simplifications back into the inequality:
\[
6x - 8 > 9x - 18
\]

### Step 3: Rearranging the terms

To isolate \( x \), subtract \( 6x \) from both sides:
\[
-8 > 3x - 18
\]

Now, add \( 18 \) to both sides:
\[
10 > 3x
\]

### Step 4: Divide by 3

Now divide both sides by \( 3 \) (since \( 3 > 0 \), the inequality remains the same):
\[
\frac{10}{3} > x
\]
or equivalently,
\[
x < \frac{10}{3}
\]

### Solution

Thus, the solution to the inequality \( 5x + (x - 8) > \frac{9}{2}(2x - 4) \) is:
\[
x < \frac{10}{3}
\]

In interval notation, the solution is:
\[
(-\infty, \frac{10}{3})
\]