High School

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Which of the following represents "7 is at most the difference of a number and 5"?

A. [tex]7 \leq x - 5[/tex]

B. [tex]7 \gt x - 5[/tex]

C. [tex]7 \leq 5 - x[/tex]

D. [tex]7 \gt 5 - x[/tex]

Answer :

To solve the problem, we need to interpret the statement "7 is at most the difference of a number and 5." This can be expressed mathematically as:

1. [tex]\( 7 \leq x - 5 \)[/tex]

Now, let's solve the inequality:

1. Start with the inequality:
[tex]\( 7 \leq x - 5 \)[/tex]

2. To isolate [tex]\( x \)[/tex], add 5 to both sides of the inequality:
[tex]\( 7 + 5 \leq x \)[/tex]

3. Simplify the left side:
[tex]\( 12 \leq x \)[/tex] or [tex]\( x \geq 12 \)[/tex]

This means that the number [tex]\( x \)[/tex] must be greater than or equal to 12. Therefore, the solution to the inequality is [tex]\( x \geq 12 \)[/tex].

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