Which expressions are equivalent to 10p - 18? Select TWO correct answers.
Understand the Problem
The question is asking which expressions are equivalent to the expression 10p - 18. The goal is to select two correct answers from the given options based on algebraic manipulation.
Answer
$\frac{1}{2}(20p - 36)$ and $2(5p - 9)$
Answer for screen readers
The two expressions equivalent to $10p - 18$ are:
- $\frac{1}{2}(20p - 36)$
- $2(5p - 9)$
Steps to Solve
-
Identify the Target Expression We are looking for expressions that are equivalent to $10p - 18$.
-
Simplify Each Option We'll simplify each given expression to check for equivalence.
-
Option 1: $\frac{1}{2}(20p - 36)$
- Distributing $\frac{1}{2}$: $$ \frac{1}{2} \cdot 20p - \frac{1}{2} \cdot 36 = 10p - 18 $$
- This matches our target expression.
-
Option 2: $2(5p + 9)$
- Distributing $2$: $$ 2 \cdot 5p + 2 \cdot 9 = 10p + 18 $$
- This does not match our target expression.
-
Option 3: $\frac{1}{2}(5p - 9)$
- Distributing $\frac{1}{2}$: $$ \frac{1}{2} \cdot 5p - \frac{1}{2} \cdot 9 = \frac{5p}{2} - \frac{9}{2} $$
- This does not match our target expression.
-
Option 4: $2(5p - 9)$
- Distributing $2$: $$ 2 \cdot 5p - 2 \cdot 9 = 10p - 18 $$
- This matches our target expression.
-
Option 5: $2(5p)$
- Distributing $2$: $$ 2 \cdot 5p - 2 \cdot 9 = 10p - 18 $$
- This matches our target expression.
-
-
Conclusion of Options The two expressions equivalent to $10p - 18$ are:
- Option 1: $\frac{1}{2}(20p - 36)$
- Option 4: $2(5p - 9)$
The two expressions equivalent to $10p - 18$ are:
- $\frac{1}{2}(20p - 36)$
- $2(5p - 9)$
More Information
Both selected expressions simplify to the same original expression by correctly applying the distributive property. This demonstrates the concept of expression equivalence through algebraic manipulation.
Tips
- Confusing the signs when distributing, particularly with negatives (e.g., turning $-9$ into $+9$).
- Failing to simplify correctly, especially if not fully applying the distribution step.