Scenario: Phone Plans - Learn to simplify algebraic expressions by comparing phone plan costs!
Compare two phone plans:
Let x = number of minutes used. Find the difference in cost between the plans.
Cost expressions:
Plan A: 50 + 0.1x
Plan B: 30 + 0.2x
Difference: (50 + 0.1x) - (30 + 0.2x)
Step 1: Remove parentheses using distributive property
(50 + 0.1x) - (30 + 0.2x) = 50 + 0.1x - 30 - 0.2x
Step 2: Combine like terms
50 + 0.1x - 30 - 0.2x = (50 - 30) + (0.1x - 0.2x) = 20 - 0.1x
Final simplified expression: 20 - 0.1x
Distributive Property: a(b + c) = ab + ac
We can "distribute" multiplication over addition or subtraction.
3(2x + 5) = 3 × 2x + 3 × 5 = 6x + 15
4(x - 3) = 4 × x - 4 × 3 = 4x - 12
Like Terms: Terms that have the same variable raised to the same power.
Examples: 3x and 5x are like terms; 2x² and 7x² are like terms; but 3x and 2x² are NOT like terms.
Simplify: 3(2x - 5) + 4x
Step 1: Apply distributive property
3(2x - 5) + 4x = 6x - 15 + 4x
Step 2: Combine like terms
6x - 15 + 4x = (6x + 4x) - 15 = 10x - 15
Simplify: 5(3x + 2)
Your solution:
Simplify: 2x + 5 - 3x + 7
Your solution:
Simplify: 4(2x - 3) + 2(x + 1)
Your calculation: