Skill: Identify equivalent expressions

Equivalent expressions may look different but have the same value for every allowed value of the variable.

To identify equivalent expressions, rewrite one expression using properties and combine like terms.

Example: Are $3(x+4)+2x$ and $5x+12$ equivalent?

1. Distribute the $3$ to each term inside the parentheses:

$$3(x+4)+2x=3x+12+2x$$

2. Combine like terms. The terms $3x$ and $2x$ both have $x$, so add their coefficients:

$$3x+2x+12=5x+12$$

3. The expression becomes:

$$3(x+4)+2x=5x+12$$

So, $3(x+4)+2x$ and $5x+12$ are equivalent expressions.

You can check by choosing a value, such as $x=2$:

$$3(2+4)+2(2)=3(6)+4=22$$

and

$$5(2)+12=10+12=22$$

Both expressions give the same value.