Question

decide whether the equation is an identity, a conditional equation, or a contradiction. give the solution set. 5(2x - 31) = 10x - 155 a. identity; ∅ b. identity; {all real numbers} c. conditional; {0} d. contradiction; ∅

Explanation:

Step1: Expand the left side

First, we expand the left - hand side of the equation \(5(2x - 31)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 5\), \(b=2x\) and \(c=- 31\). So we have \(5\times2x-5\times31=10x - 155\).

Step2: Compare both sides

The right - hand side of the original equation is \(10x-155\). After expanding the left - hand side, we get the same expression as the right - hand side. This means that the equation \(5(2x - 31)=10x - 155\) is true for all real values of \(x\). An equation that is true for all real numbers is called an identity, and its solution set is the set of all real numbers.

Answer:

B. Identity; \{all real numbers\}