Which expressions are equivalent to 10p - 18? Select TWO correct answers.

Question image

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

  1. Identify the Target Expression We are looking for expressions that are equivalent to $10p - 18$.

  2. 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.
  3. 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.
Thank you for voting!
Use Quizgecko on...
Browser
Browser