Let's break down the problem step-by-step.
### Step 1: Write the Expression
The problem asks us to write an expression for "four less than the quotient of ten and a number, increased by eight".
- "The quotient of ten and a number" translates to [tex]\( \frac{10}{y} \)[/tex].
- "Four less than" implies subtracting 4 from this quotient, so it becomes [tex]\( \frac{10}{y} - 4 \)[/tex].
- Finally, "increased by eight" means adding 8 to the result, giving us the final expression:
[tex]\[ 4 - \left(\frac{10}{y}\right) + 8 \][/tex]
### Step 2: Substitute 2 for the Variable [tex]\( y \)[/tex]
We are given [tex]\( y = 2 \)[/tex]. Substitute this into the expression:
[tex]\[ 4 - \left(\frac{10}{2}\right) + 8 \][/tex]
### Step 3: Simplify by Using Arithmetic Operations
First, perform the division inside the parentheses:
[tex]\[ \frac{10}{2} = 5 \][/tex]
So, the expression becomes:
[tex]\[ 4 - 5 + 8 \][/tex]
Next, carry out the subtraction and addition from left to right:
[tex]\[ 4 - 5 = -1 \][/tex]
[tex]\[ -1 + 8 = 7 \][/tex]
Therefore, the final result is:
[tex]\[ 7 \][/tex]
### Conclusion
The answer is [tex]\( 7 \)[/tex]. ✔
