Problem 15 - Algebra and Trigonometry

Question

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+3 y}{x+1}, \text { for } x=-2 \text { and } y=4$$

Step-by-Step Solution

Answer

-8

Step 1: Substitute Given Values

To start, replace \(x\) with \(-2\) and \(y\) with \(4\) in the given expression. You will have \(\frac{2(-2)+3(4)}{-2+1}\).

Step 2: Perform Arithmetic Operations in the Numerator

Next, perform multiplication and addition in the numerator: \(2(-2) + 3(4)\) gives \(-4 + 12\), which is \(8\). Therefore, the revised expression becomes \(\frac{8}{-2+1}\).

Step 3: Perform Arithmetic Operations in the Denominator

Perform addition in the denominator: \(-2+1\) gives \(-1\). The revised expression now becomes \(\frac{8}{-1}\).

Step 4: Final Calculation

Finally, we perform the division, giving us a final result of \(-8\).