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What is the missing step in solving the inequality [tex] 5 \ \textless \ 8x - 2x + 3 [/tex]?

A. Add [tex] 2x [/tex] to both sides of the inequality.
B. Subtract [tex] 8x [/tex] from both sides of the inequality.
C. Subtract [tex] 2x [/tex] from both sides of the inequality.
D. Add [tex] 8x [/tex] to both sides of the inequality.

Sagot :

GinnyAnswer
To solve the inequality [tex]\(5 < 8x < 2x + 3\)[/tex], let's break down the steps in detail to identify the missing step.

1. Understand the given inequality:
We start with the compound inequality:
[tex]\[5 < 8x < 2x + 3\][/tex]

2. Isolate the term involving [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to move all terms involving [tex]\( x \)[/tex] to one side.

3. Perform the missing step:
The operation needed to isolate [tex]\( x \)[/tex] involves removing [tex]\( 2x \)[/tex] from the rightmost part of the inequality.
We need to subtract [tex]\( 2x \)[/tex] from both sides of the inequality:
[tex]\[5 < 8x - 2x < 2x + 3 - 2x\][/tex]

4. Simplify the inequality:
Simplifying the inequality after subtracting [tex]\( 2x \)[/tex]:
[tex]\[5 < 6x < 3\][/tex]

Therefore, the correct missing step in solving the inequality is to subtract [tex]\( 2x \)[/tex] from both sides of the inequality.
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