Certainly! Let's solve the inequality step by step:
Given inequality:
[tex]\[ -2(5 - 4x) < 6x - 4 \][/tex]
### Step 1: Distribute the -2 on the left side
First, we distribute the -2:
[tex]\[ -2 \cdot 5 + (-2) \cdot (-4x) < 6x - 4 \][/tex]
[tex]\[ -10 + 8x < 6x - 4 \][/tex]
### Step 2: Combine like terms by moving all [tex]\( x \)[/tex] terms to one side
Next, we isolate the [tex]\( x \)[/tex] terms by subtracting [tex]\( 6x \)[/tex] from both sides:
[tex]\[ 8x - 6x < -4 + 10 \][/tex]
[tex]\[ 2x < 6 \][/tex]
### Step 3: Divide both sides by 2 to solve for [tex]\( x \)[/tex]
Finally, we solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ \frac{2x}{2} < \frac{6}{2} \][/tex]
[tex]\[ x < 3 \][/tex]
So, the final step leads us to the solution:
[tex]\[ x < 3 \][/tex]
Among the given options:
- [tex]\( x < -3 \)[/tex]
- [tex]\( x > -3 \)[/tex]
- [tex]\( x < 3 \)[/tex]
- [tex]\( x > 3 \)[/tex]
The correct answer is:
[tex]\[ x < 3 \][/tex]
