Question

Use the distributive property to write an equivalent variable expression.

$-4 (2n-7)$

Short answer

$- \text{4} \text{(2n} - \text{7} \text{)} = - 8n + 28$.

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

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. $- \text{4} · - \text{7} = + 28$

Distributive Property of Multiplication

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

$\begin{array}{l}-\text{\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}(2n\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}7\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=-\text{\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}}·2n-\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}}·-7=-8n+28\\ -\text{\hspace{0.17em}\hspace{0.17em}4\hspace{0.17em}(2n\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}7\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}=-8n+28\end{array}$