To determine which equation best represents the given statement, let's break down the statement and analyze each option step-by-step.
The statement reads:
"Negative five-sixths times the sum of a number and six and two-tenths is seven and five-tenths."
First, let's convert the statement into a mathematical form:
- "Negative five-sixths" is [tex]\(-\frac{5}{6}\)[/tex].
- "The sum of a number and six and two-tenths" is [tex]\(x + 6.2\)[/tex].
- "Is seven and five-tenths" translates to [tex]\(= 7.5\)[/tex].
Combining these, we get:
[tex]\[ -\frac{5}{6} \times (x + 6.2) = 7.5 \][/tex]
Now we need to identify which of the provided equations matches this form:
1. [tex]\( -\frac{5}{6}(x + 6.2) = 7.5 \)[/tex]
2. [tex]\( -\frac{5}{6} + 6.2 x = 7.5 \)[/tex]
3. [tex]\( -\frac{5}{6} x + 6.2 = 7.5 \)[/tex]
4. [tex]\(\left(-\frac{5}{6} + x\right) \times 6.2 = 7.5 \)[/tex]
Let’s analyze each:
1. [tex]\( -\frac{5}{6}(x + 6.2) = 7.5 \)[/tex]
- This matches our derived equation directly. So, this is a possible correct option.
2. [tex]\( -\frac{5}{6} + 6.2 x = 7.5 \)[/tex]
- This does not match our derived equation because it does not follow the structure of "negative five-sixths times the sum of a number and six and two-tenths."
3. [tex]\( -\frac{5}{6} x + 6.2 = 7.5 \)[/tex]
- This does not match our derived equation either, as it separates [tex]\( 6.2 \)[/tex] instead of being added inside the parenthesis with [tex]\( x \)[/tex].
4. [tex]\(\left(-\frac{5}{6} + x\right) \times 6.2 = 7.5 \)[/tex]
- This again does not match our derived equation because the placement of [tex]\( x \)[/tex] and [tex]\( 6.2 \)[/tex] do not follow the given statement.
Therefore, the equation that best represents the given statement is:
[tex]\[ -\frac{5}{6}(x + 6.2) = 7.5 \][/tex]
So, the corresponding option from the given choices is:
[tex]\[ -\frac{5}{6}(x + 6.2) = 7.5 \][/tex]
The correct option is the first one (index 0).
