Virginia SOL Math / Grade 7 / Patterns, Functions & Algebra
Equivalent Algebraic Expressions
What you'll learn
- Simplify expressions by combining like terms
- Apply the distributive property
- Generate equivalent expressions
Words to know
- Term —
- a number, a variable, or their product in an expression
- Like terms —
- terms with the same variable raised to the same power
- Coefficient —
- the number multiplied by a variable
- Distributive property —
- a rule that multiplies a factor across a sum or difference
- Equivalent expressions —
- expressions that have the same value for every variable value
Why it matters Simplifying expressions makes equations easier to read and solve, which is the foundation of all the algebra that follows.
Worked examples
Model ItI do
Simplify 3x + 5x.
These are like terms, so add the coefficients: 3 + 5 = 8. The simplified expression is 8x.
Try It TogetherWe do
Use the distributive property to expand 4 times the quantity x + 2.
Multiply 4 by each term inside: 4 times x = 4x and 4 times 2 = 8. The result is 4x + 8.
Now YouYou do
Simplify 7y minus 2y + 4.
Combine the like terms with y, then keep the constant. Check your answer in the back of this chapter.
Practice
Mastered 0 of 11
Warm-up
Ease in with the basics.
1.Simplify 4x + 3x.
2.Expand 2 times the quantity x + 3.
3.Simplify 8m minus 3m.
On Level
The core Quick Check from the book.
1.Simplify 6a + 2a.
2.Expand 3 times the quantity x + 5.
3.Simplify 9m minus 4m.
4.Combine like terms: 2x + 7 + 3x.
5.Expand 5 times the quantity 2x minus 1.
Challenge
Stretch your thinking.
1.Simplify 5x + 2 + 3x minus 4.
2.Expand and simplify 3 times the quantity 2x + 4, then add x.
3.Simplify 6 times the quantity x minus 2 minus 2 times the quantity x + 1.