%2B(x%2B4)%2B(x%2B7).jpeg "(x+1)+(x+4)+(x+7)")
Simplifying the Expression (x+1) + (x+4) + (x+7)
This expression involves adding three binomials together. Let's break down how to simplify it:
Understanding the Expression
- Binomials: Each part of the expression, (x+1), (x+4), and (x+7), is called a binomial because it contains two terms: a variable term (x) and a constant term (1, 4, or 7).
Combining Like Terms
To simplify the expression, we combine like terms. This means:
- Combining 'x' terms: We add the coefficients of the 'x' terms: 1x + 1x + 1x = 3x
- Combining constant terms: We add the constant terms: 1 + 4 + 7 = 12
Simplified Expression
After combining like terms, the simplified expression is:
3x + 12
Example:
Let's say x = 2. We can substitute this value into both the original expression and the simplified expression to see if they give the same answer:
Original Expression: (2+1) + (2+4) + (2+7) = 3 + 6 + 9 = 18
Simplified Expression: 3(2) + 12 = 6 + 12 = 18
As you can see, both expressions result in the same answer (18) when x = 2. This demonstrates that the simplified expression is equivalent to the original expression.