Question

Use the distributive property to write an equivalent variable expression.

$- 2 ( 3 - r )$

Short answer

$- 2(3-r)= - 6 + 2r = 2r - 6$.

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

Example: $-\text{3} \text{(8} - \text{5} \text{)} = (-\text{3} ) · 8 - (-\text{3} ) · \text{5} = -24+15=- 9$

Step-3:  Use the distributive property to evaluate the expression.

We know that double negative is always positive. $-2 · (- r) = + 2r$

Distributive Property of Multiplication

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

localid="1649343437037" $\begin{array}{l}-2(3-r)=-2·3-2·(-r\text{\hspace{0.17em})\hspace{0.17em}}=-6+2r=2r-6\\ -2(3-r)=-6+2r=2r-6\end{array}$