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Step 1: [tex]\(-10 + 8x \ \textless \ 6x - 4\)[/tex]
Step 2: [tex]\(-10 \ \textless \ -2x - 4\)[/tex]
Step 3: [tex]\(-6 \ \textless \ -2x\)[/tex]
Step 4: [tex]\(\frac{-6}{-2} \ \textgreater \ x\)[/tex]
Step 5: [tex]\(x \ \textgreater \ 3\)[/tex]

What is the final step in solving the inequality [tex]\(-10 + 8x \ \textless \ 6x - 4\)[/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 :

GinnyAnsweridn
To solve the inequality [tex]\(-2(5 - 4x) < 6x - 4\)[/tex], let's work through each of the steps given:

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

This is already provided. The initial inequality is simplified to this form.

Step 2: [tex]\(-10 < -2x - 4\)[/tex]

To isolate the [tex]\(x\)[/tex] terms, subtract [tex]\(6x\)[/tex] from both sides, which simplifies to this step.

Step 3: [tex]\(-6 < -2x\)[/tex]

Next, add 4 to both sides of the inequality:

[tex]\[ -10 + 4 < -2x \][/tex]

This simplifies to:

[tex]\[ -6 < -2x \][/tex]

Step 4: Divide both sides by -2 and reverse the inequality sign.

When you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign. So, dividing both sides of [tex]\(-6 < -2x\)[/tex] by [tex]\(-2\)[/tex]:

[tex]\[ \frac{-6}{-2} > x \][/tex]

Which simplifies to:

[tex]\[ 3 > x \][/tex]

Or, equivalently:

[tex]\[ x < 3 \][/tex]

Therefore, the correct final step and solution to the inequality is [tex]\(x < 3\)[/tex].

So the correct answer is:

[tex]\[ x < 3 \][/tex]
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