Question

Simplify the expression by arranging the steps in sequence, based on the order of operations.

a) 1/6 [30x + 24] - 1/7 [63 - 7x]
b) Distribute the constants: (1/6 * 30x + 1/6 * 24) - (1/7 * 63 - 1/7 * 7x)
c) Simplify further: (5x + 4) - (9 - x)
d) Combine like terms: 5x + x + 4 - 9
e) Final simplification: 6x - 5 = 6x - 5

Answer 1

To simplify the algebraic expression, distribute the constants, simplify multiplication, combine like terms, and arrive at the simplified expression 6x - 5. Check the answer for reasonableness.

Step-by-step explanation:

To simplify the expression given in the question, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). We'll start by distributing the constants within the parentheses and then combining like terms.

Step-by-step simplification:

1. Distribute the constants: (1/6 * 30x + 1/6 * 24) - (1/7 * 63 - 1/7 * 7x).
2. Simplify the multiplication: (5x + 4) - (9 - x).
3. Combine like terms: 5x + x + 4 - 9.
4. Final simplification: 6x - 5 = 6x - 5.

After these steps, we arrive at the final simplified expression, which is 6x - 5.

Additionally, we check the answer to ensure it is reasonable and doesn't contain any mistakes.