Solving the Expression 4a - 2b / -c with Given Values: A Step-by-Step Guide
When given the values a -2, b 4, and c -6, how do you solve the expression 4a - 2b / -c? This guide will break down the steps involved in solving this algebraic expression step-by-step using clear and concise instructions. Let's dive in!
Step-by-Step Solution
Given the equation:
4a - 2b / -c with:
a -2, b 4, c -6
We know that a -2 and b 4. We will substitute these values into the equation: Calculate 4a:
4a 4 × -2 -8 Calculate -2b:
-2b -2 × 4 -8 Add the results from steps 2 and 3:
4a - 2b -8 (-8) -16 Calculate -c:
For c -6, the negative of c is -(-6) 6. Divide the results from steps 4 and 5:
frac{4a - 2b}{-c} frac{-16}{6} Simplify the fraction:
frac{-16}{6} frac{-8}{3}
Therefore, the final result is:
boxed{frac{-8}{3}}Alternative Methods of Solving
Here are a few different ways to approach the same problem:
Original Method:{4-2 - 24 / --6} {-8 - 8 / 6} - frac{16}{6} Another Approach:
- frac{8}{6} - frac{8}{6} - frac{16}{6} Further Simplification:
- frac{16}{6} - frac{8}{3}
The fraction can also be reduced to its simplest form, -8/3. This can be approximated to -2.666 or -2 2/3.
Understanding the Process
To understand the process better, let's break it down further:
Breaking down the expression:4a - 2b / -c 4 × -2 - 2 × 4 / -6 Calculate 4 × -2 and 2 × 4:
4-2 -8
-24 -8 Add -8 and -8:
-8 - 8 -16 Calculate -(-6):
-c --6 6 Divide -16 by 6:
- frac{16}{6} - frac{8}{3}
Thus, the final result remains - frac{8}{3}.
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**Keywords:** math expression, algebraic substitution, solving equations