Answered

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The inequality [tex]-2x \ \textless \ -3(x - 5)[/tex] is equivalent to which of the following inequalities?

A) [tex]x \ \textgreater \ -15[/tex]
B) [tex]x \ \textless \ 15[/tex]
C) [tex]x \ \textgreater \ 15[/tex]
D) [tex]x \ \textless \ -7[/tex]

Sagot :

GinnyAnswer
To solve the given inequality, [tex]\(-2x < -3(x - 5)\)[/tex], let's follow a step-by-step approach:

1. Distribute on the right side:
[tex]\[ -2x < -3(x - 5) \][/tex]
Distribute the [tex]\(-3\)[/tex] across the terms inside the parentheses:
[tex]\[ -2x < -3x + 15 \][/tex]

2. Move all [tex]\(x\)[/tex] terms to one side:
To isolate [tex]\(x\)[/tex], add [tex]\(3x\)[/tex] to both sides of the inequality:
[tex]\[ -2x + 3x < -3x + 3x + 15 \][/tex]
Simplify the inequality:
[tex]\[ x < 15 \][/tex]

So, the inequality [tex]\(-2x < -3(x-5)\)[/tex] simplifies to [tex]\(x < 15\)[/tex].

Thus, the correct answer is:

B) [tex]\(x < 15\)[/tex]
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