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What is the value of this expression when [tex]\( a=7 \)[/tex] and [tex]\( b=-4 \)[/tex]?

[tex]\[
\frac{|2a| - b}{3}
\][/tex]

A. -6
B. [tex]\(-3 \frac{1}{3}\)[/tex]
C. [tex]\(3 \frac{1}{3}\)[/tex]
D. 6

Sagot :

GinnyAnswer
To find the value of the expression [tex]\(\frac{|2 a| - b}{3}\)[/tex] for [tex]\(a = 7\)[/tex] and [tex]\(b = -4\)[/tex], follow these steps:

1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- [tex]\(a = 7\)[/tex]
- [tex]\(b = -4\)[/tex]

2. Calculate the inside expressions:
- Calculate [tex]\(2a\)[/tex]:
[tex]\[ 2 \cdot 7 = 14 \][/tex]
- Calculate the absolute value of [tex]\(2a\)[/tex]:
[tex]\[ |2 \cdot 7| = |14| = 14 \][/tex]
- Calculate [tex]\(-b\)[/tex]:
[tex]\[ -(-4) = 4 \][/tex]

3. Substitute these results into the numerator [tex]\(|2a| - b\)[/tex]:
[tex]\[ 14 + 4 = 18 \][/tex]

4. Divide the numerator by 3 to find the value of the expression:
[tex]\[ \frac{18}{3} = 6 \][/tex]

Therefore, the value of the expression is 6.

So, the correct answer is:
[tex]\[ \boxed{6} \][/tex]
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