Question

determine if each pair of expressions are equivalent.

• $2(x + 8) + 3$
• $2x + 19$

options: yes, no

Explanation:

Step1: Expand the first expression

Using the distributive property \(a(b + c)=ab + ac\), for \(2(x + 8)\), we get \(2\times x+2\times8 = 2x + 16\). Then add 3: \(2x+16 + 3\).

Step2: Simplify the first expression

Combine like terms: \(2x+(16 + 3)=2x + 19\).

Step3: Compare the two expressions

The first expression simplifies to \(2x + 19\), which is the same as the second expression \(2x + 19\).

Answer:

Yes