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What is the missing step in solving the inequality [tex]5 + 8x \ \textless \ 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 :

GinnyAnsweridn
To determine the missing step in solving the given inequality:

[tex]\[ 5 < 8x < 2x + 3 \][/tex]

we need to isolate the variable [tex]\( x \)[/tex]. Let's proceed step-by-step:

1. Initially, the inequality is given as:
[tex]\[ 5 < 8x < 2x + 3 \][/tex]

2. We can break this into two separate inequalities for simplicity:
[tex]\[ 5 < 8x \][/tex]
[tex]\[ 8x < 2x + 3 \][/tex]

Focus on the second inequality:
[tex]\[ 8x < 2x + 3 \][/tex]

3. To isolate [tex]\( x \)[/tex], we need to move all terms involving [tex]\( x \)[/tex] to one side. A key step in solving this is to eliminate the [tex]\( 8x \)[/tex] on the left side.

4. Subtract [tex]\( 8x \)[/tex] from both sides to remove [tex]\( 8x \)[/tex] from the left:
[tex]\[ 8x - 8x < 2x + 3 - 8x \][/tex]

This simplifies to:
[tex]\[ 0 < -6x + 3 \][/tex]

So the necessary step to solve the inequality is:

Subtract [tex]\( 8x \)[/tex] from both sides of the inequality.

Thus, the correct answer is:
[tex]\[ \boxed{\text{Subtract } 8x \text{ from both sides of the inequality.}} \][/tex]
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