simplify: 3/5x + x Where 3 over 5 x plus x
The Correct Answer and Explanation is:
Simplified Expression:
35x+x=85x\frac{3}{5}x + x = \frac{8}{5}x
Explanation
Let’s break down the expression: 35x+x\frac{3}{5}x + x
This expression involves like terms. “Like terms” are terms that have the same variable raised to the same power—in this case, both terms include the variable x to the first power.
Now, let’s write x in fraction form so it’s easier to add it to 35x\frac{3}{5}x. Remember, x is the same as 55x\frac{5}{5}x, because 55=1\frac{5}{5} = 1. So: 35x+x=35x+55x\frac{3}{5}x + x = \frac{3}{5}x + \frac{5}{5}x
Now that both terms have the same denominator, we can add the numerators: (3+55)x=85x\left(\frac{3 + 5}{5}\right)x = \frac{8}{5}x
So, the simplified form of 35x+x\frac{3}{5}x + x is: 85x\frac{8}{5}x
Why This Matters:
Understanding how to simplify expressions like this is essential in algebra because it prepares you to solve equations, analyze functions, and work with formulas in science and engineering.
You always want to combine like terms where possible, because simpler expressions are easier to work with. The key steps are:
- Recognize like terms (they must have the same variable and power).
- If needed, convert whole numbers to fractions to have a common denominator.
- Add or subtract the coefficients (the numbers in front of the variables).
- Keep the variable part unchanged.
In this case, we added the coefficients 35\frac{3}{5} and 11 (written as 55\frac{5}{5}), which gave 85\frac{8}{5}. The variable x stays the same, since we are only combining its coefficients.
This is a fundamental algebra skill used throughout higher-level math.
