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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]3 \ \textgreater \ x[/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], follow these detailed steps:

Step 1: Distribute [tex]\(-2\)[/tex] on the left side of the inequality:
[tex]\[ -2(5 - 4x) < 6x - 4 \][/tex]
[tex]\[ -2 \cdot 5 + (-2) \cdot (-4x) < 6x - 4 \][/tex]
[tex]\[ -10 + 8x < 6x - 4 \][/tex]

Step 2: Move all [tex]\(x\)[/tex] terms to one side and constants to the other side:
[tex]\[ -10 + 8x < 6x - 4 \][/tex]
Subtract [tex]\(6x\)[/tex] from both sides:
[tex]\[ 8x - 6x < -4 + 10 \][/tex]
[tex]\[ 2x < 6 \][/tex]

Step 3: Isolate [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[ \frac{2x}{2} < \frac{6}{2} \][/tex]
[tex]\[ x < 3 \][/tex]

Therefore, the final step in solving the inequality [tex]\(-2(5 - 4x) < 6x - 4\)[/tex] is:

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

So, the correct answer is:
[tex]\[ x < 3 \][/tex]
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