Problem 117 - Algebra and Trigonometry

Question

Use the order of operations to simplify each expression. $$\frac{2(-2)-4(-3)}{5-8}$$

Step-by-Step Solution

Answer

The simplified form of given expression is \(-\frac{8}{3}\).

Step 1: Handle the Numerators and Denominators Separately

First, we'll evaluate the expression in the numerator and the denominator separately. The numerator is \(2(-2)-4(-3)\) and the denominator is \(5-8\).

Step 2: Apply Order of Operations in the Numerator

Starting with the numerator, we'll use PEMDAS/BODMAS order i.e., multiplication first then subtraction: \(2\times(-2) -4\times(-3)\) which then simplifies to \(-4 - (-12)\). Finally, subtraction gives the result as \(-4 + 12 = 8\).

Step 3: Solve the Denominator

The denominator operation is simple subtraction: \(5 - 8\), which equals to \(-3\).

Step 4: Divide Numerator by Denominator

The final step is to divide the numerical value from the numerator (which is 8) by the numerical value obtained in the denominator (which is -3). So, our final answer is \(-\frac{8}{3}\).