What is 2y-1 increased by 9y+19?
The correct answer and explanation is:
The expression “2y – 1 increased by 9y + 19” can be simplified by adding the two expressions together.
- Start by writing the two expressions: 2y−1and9y+192y – 1 \quad \text{and} \quad 9y + 19
- To add the expressions, combine the like terms. Like terms are those that have the same variable. In this case, both terms involving yy (i.e., 2y2y and 9y9y) are like terms, and the constant terms −1-1 and 1919 are also like terms.
- Add the terms involving yy: 2y+9y=11y2y + 9y = 11y
- Add the constant terms: −1+19=18-1 + 19 = 18
- Now, combine the results: 11y+1811y + 18
Thus, the sum of 2y−12y – 1 increased by 9y+199y + 19 is: 11y+1811y + 18
Explanation:
When dealing with expressions like this, the key is to identify like terms and combine them correctly. In algebra, “increased by” typically means to add. For example, the expression “2y – 1 increased by 9y + 19” involves adding two algebraic expressions. The operation of addition is straightforward: you combine the coefficients of like terms (the terms involving yy) and separately add the constant terms. This results in a simplified expression where the variable terms are combined into a single term and the constants are added together.