Question

solving equations with the distributive property - item 992452 question 5 of drag each equation to show if it could be a correct first step to solving the equation 2(x + 7) = 36. 2(x + 7) = 72 2x + 7 = 36 2x + 14 = 36 (2·x) + (2·7) = 36 x + 7 = 18 x + 14 = 36 yes no not enough information drag and drop items here drag and drop items here drag and drop items here

Explanation:

Step1: Recall Distributive Property

The distributive property is \(a(b + c)=ab + ac\). For the equation \(2(x + 7)=36\), applying the distributive property: \(2\times x+2\times7 = 36\), which is \((2\cdot x)+(2\cdot7)=36\) or \(2x + 14=36\). Also, dividing both sides by 2: \(\frac{2(x + 7)}{2}=\frac{36}{2}\), so \(x + 7=18\).

Step2: Analyze Each Equation

• \(2(x + 7)=72\): Original equation is \(2(x + 7)=36\), this multiplies RHS by 2, incorrect.
• \(2x + 7=36\): Distributive property was applied incorrectly (7 not multiplied by 2), incorrect.
• \(2x + 14=36\): Correct (distributive property: \(2(x + 7)=2x+14\)).
• \((2\cdot x)+(2\cdot7)=36\): Correct (distributive property).
• \(x + 7=18\): Correct (dividing both sides by 2).
• \(x + 14=36\): Incorrect (wrong operation, not dividing or distributing correctly).

Answer:

Yes: \(2x + 14 = 36\), \((2\cdot x)+(2\cdot7)=36\), \(x + 7 = 18\)
No: \(2(x + 7)=72\), \(2x + 7 = 36\), \(x + 14 = 36\)
Not Enough Information: None (all can be analyzed with given info)