1. Use properties of operations to determine whether or not 2.5(1+x) and 0.5x+2.5x are equivalent. 2. Simplify the expression 8x+4+2x+3.
Understand the Problem
The first question asks to determine whether two expressions are equivalent using the properties of operations. The expressions are 2.5(1+x) and 0.5x + 2.5x. The second question asks you to simplify the expression 8x + 4 + 2x + 3 by combining like terms.
Answer
12. Not equivalent 13. $10x + 7$
Answer for screen readers
- The expressions $2.5(1+x)$ and $0.5x + 2.5x$ are not equivalent.
- The simplified expression is $10x + 7$.
Steps to Solve
- Distribute 2.5 in the first expression
Apply the distributive property to $2.5(1+x)$. This means multiplying 2.5 by both 1 and $x$. $2.5(1+x) = 2.5 * 1 + 2.5 * x = 2.5 + 2.5x$
- Combine like terms in the second expression
Combine the $x$ terms in $0.5x + 2.5x$. $0.5x + 2.5x = (0.5 + 2.5)x = 3x$
- Compare the simplified expressions
The simplified expressions are $2.5 + 2.5x$ and $3x$. They are not the same.
- Combine like terms in the expression to simplify
Combine the $x$ terms: $8x + 2x = 10x$. Combine the constant terms: $4 + 3 = 7$.
- Write the simplified expression
The simplified expression is $10x + 7$.
- The expressions $2.5(1+x)$ and $0.5x + 2.5x$ are not equivalent.
- The simplified expression is $10x + 7$.
More Information
The distributive property is key to expanding expressions, and combining like terms helps simplify them.
Tips
A common mistake is incorrectly applying the distributive property. For example, not multiplying the 2.5 by both terms in the parentheses. Also, mistakes may happen when combining the like terms.
AI-generated content may contain errors. Please verify critical information
