Question

Are $2(x+1) \text{and} 2x+1$ equivalent variable expressions? Explain.

Short answer

The two expressions are not same & they are not equivalent

Step-by-step solution

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

Step-2 – Distributive Property of Multiplication 

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property: $\text{a} \text{(b} \text{+} \text{c} \text{)} = \text{a} · \text{b} + \text{a} · \text{c}$

Example: $12 \text{(3} \text{+} \text{4} \text{)} 12= \text{12} · \text{3} + \text{12} · \text{4} = 36 + 48 = 84$

Step-3:  Are 2(x+1) and 2x+1 equivalent variable expressions? Explain.

Using distributive property of multiplication

Property: $\text{a} \text{(b} \text{+} \text{c} \text{)} = \text{a} · \text{b} + \text{a} · \text{c}$

We can write by using distributive method of multiplication:$2\left(x+1\right)$= $2x+2$

The second expression is $2\left(x+1\right)$

Since this two expressions are not same & they are not equivalent.