Answered

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Step 1: [tex]\(-10 + 8x \ \textless \ 6x - 4\)[/tex]

Step 2: [tex]\(2x \ \textless \ 6\)[/tex]

Step 3: [tex]\(x \ \textless \ 3\)[/tex]

What is the final step in solving the inequality [tex]\(-2(5 - 4x) \ \textless \ 6x - 4\)[/tex]?

A. [tex]\(x \ \textless \ -3\)[/tex]
B. [tex]\(x \ \textgreater \ -3\)[/tex]
C. [tex]\(x \ \textless \ 3\)[/tex]
D. [tex]\(x \ \textgreater \ 3\)[/tex]

Sagot :

GinnyAnswer
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]
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