Question
\[ \begin{array}{l} \text { (x } 2(x+7)+3 x=12 \text { (given) } \\ \quad 2 x+14+3 x=12 \text { (?) } \\ 5 x+14=12 \text { (simplify) } \\ 5 x=-2 \text { (subtraction) } \\ x=-\frac{2}{5} \text { (division) } \end{array} \] What is the missing reason? A Addition B Subtraction C Reflexive Property D Transitive Property E Distributive Property
Ask by Todd Warner. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The missing reason is the Distributive Property.
Solution
The missing step involves expanding the expression \( 2(x + 7) \). To go from \( 2(x + 7) + 3x = 12 \) to \( 2x + 14 + 3x = 12 \), you apply the **Distributive Property**, which states that \( a(b + c) = ab + ac \).
**Answer:**
E Distributive Property
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
The missing reason in the given equation is E Distributive Property. The first line shows an expression that involves distributing \(2\) into the sum \((x + 7)\), resulting in \(2x + 14\) before moving on to the next steps. To clarify the steps leading to \(5x + 14 = 12\), after applying the Distributive Property, you combine like terms to ultimately get your simplified expression.
