To evaluate an expression for specific values of \( x \) without simplifying first, you can substitute the values directly into the expression.
Let's say we have an arbitrary equation (for demonstration), such as:
\[ y = 3x^2 + 4x - 5 \]
Evaluating for \( x = 2 \):
- Substitute \( x = 2 \) into the equation:
\[ y = 3(2)^2 + 4(2) - 5 \]
This means we directly plug in \( 2 \) for \( x \).
Evaluating for \( x = 5 \):
- Substitute \( x = 5 \) into the equation:
\[ y = 3(5)^2 + 4(5) - 5 \]
Now we'll compute the result for both values but we'll follow through without simplifying the whole expression at once.
Final calculations:
For \( x = 2 \):
\[ y = 3(2)^2 + 4(2) - 5 \ = 3(4) + 4(2) - 5 \ = 12 + 8 - 5 \ = 20 - 5 \ = 15 \]
Thus, when \( x = 2 \), \( y = 15 \).
For \( x = 5 \):
\[ y = 3(5)^2 + 4(5) - 5 \ = 3(25) + 4(5) - 5 \ = 75 + 20 - 5 \ = 95 - 5 \ = 90 \]
Thus, when \( x = 5 \), \( y = 90 \).
Summary of Results:
- For \( x = 2 \), \( y = 15 \)
- For \( x = 5 \), \( y = 90 \)
This method allows you to see the steps of evaluation without first simplifying the whole equation into a single numeric expression.