Question

Solve:6(y + 4) = 6y + 10

a) y = 10
b) y = 24
c) infinitely many solutions
d) no solutions

Answer 1

d) No solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Distributive Property

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients

Explanation:

Step 1: Define

6(y + 4) = 6y + 10

Step 2: Solve for y

1. [Distributive Property] Distribute 6: 6y + 24 = 6y + 10
2. [Subtraction Property of Equality] Subtract 6y on both sides: 24 ≠ 10

Here we see that 24 does not equal 10.

∴ There are no solutions.