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Solve the following inequality: [tex]$38 \ \textless \ 4x + 3 + 7 - 3x$[/tex].

A. [tex][tex]$x \ \textless \ 28$[/tex][/tex]

B. [tex]$x \ \textless \ 4$[/tex]

C. [tex]$x \ \textgreater \ 4$[/tex]

D. [tex][tex]$x \ \textgreater \ 28$[/tex][/tex]



Answer :

GinnyAnswer
To solve the inequality [tex]\(38 < 4x + 3 + 7 - 3x\)[/tex], follow these steps:

1. Combine like terms on the right side of the inequality:
[tex]\[ 4x + 3 + 7 - 3x \][/tex]
Combine [tex]\(4x\)[/tex] and [tex]\(-3x\)[/tex], and combine the constants [tex]\(3\)[/tex] and [tex]\(7\)[/tex]:
[tex]\[ 4x - 3x + 3 + 7 = x + 10 \][/tex]

2. Rewrite the inequality with the simplified expression:
[tex]\[ 38 < x + 10 \][/tex]

3. Isolate [tex]\(x\)[/tex] by subtracting 10 from both sides:
[tex]\[ 38 - 10 < x \][/tex]
Simplify further:
[tex]\[ 28 < x \][/tex]
This can also be rewritten as:
[tex]\[ x > 28 \][/tex]

4. Identify the correct answer choice:
The inequality [tex]\(x > 28\)[/tex] matches with option D.

Therefore, the correct answer is:

D. [tex]\(x > 28\)[/tex]

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