To rewrite the expression [tex]\( 2 + 5 \times 4 - 2 \)[/tex] such that its value equals 12, we need to add parentheses in a way that changes the order of operations.
Let's look at how we can place the parentheses:
1. The given expression is [tex]\( 2 + 5 \times 4 - 2 \)[/tex].
2. By default, multiplication and division take precedence over addition and subtraction, so the expression evaluates as follows without any parentheses:
[tex]\[
2 + (5 \times 4) - 2 = 2 + 20 - 2 = 20
\][/tex]
which is not equal to 12. So, we need to change the order using parentheses.
3. Let's explore different ways to place parentheses:
Option 1: [tex]\((2 + 5) \times 4 - 2\)[/tex]
[tex]\[
(2 + 5) \times 4 - 2 = 7 \times 4 - 2 = 28 - 2 = 26
\][/tex]
which gives 26, not 12.
Option 2: [tex]\(2 + (5 \times 4) - 2\)[/tex]
[tex]\[
2 + (5 \times 4) - 2 = 2 + 20 - 2 = 20
\][/tex]
which gives 20, not 12.
Option 3: [tex]\(2 + 5 \times (4 - 2)\)[/tex]
[tex]\[
2 + 5 \times (4 - 2) = 2 + 5 \times 2 = 2 + 10 = 12
\][/tex]
which gives 12.
Therefore, the correct placement of parentheses to rewrite the expression so that its value is 12 is:
[tex]\[
2 + 5 \times (4 - 2)
\][/tex]
