Skill: Translate algebraic expressions into words

An algebraic expression is a number phrase. To translate it into words:

• A letter, such as $x$, is read as “a number” or “$x$.”
• A number beside a letter means multiplication: $(4x)$ means “four times $x$.”
• Parentheses show a group that should be kept together.
• A number outside parentheses multiplies the entire group.
• A minus sign means “minus” or “the difference between.”
• A fraction beside a variable means that fraction times the variable.

For example, translate:

$$4(x-3)+\frac{1}{2}x+7$$

Step by step:

1. The parentheses contain $(x-3)$, which means “the difference between $x$ and 3.”
2. The 4 is outside the parentheses, so it multiplies the whole group: “four times the difference between $x$ and 3.”
3. The term $\frac{1}{2}x$ means “one-half of $x$.”
4. The $(+7)$ means “plus 7.”

The complete translation is:

Four times the difference between $x$ and 3, plus one-half of $x$, plus 7.

Be careful not to say “four times $x$ minus 3.” That would describe $(4x-3)$, which is a different expression.