Q51. - Algebra 1

Question

Which value of $b$ serves as a counterexample to the statement $\mathbf{2}\mathbf{b}<\mathbf{3}\mathbf{b}$?

A. $-\mathbf{4}$     C. $\frac{1}{2}$

B. $\frac{1}{4}$      D. 4

Step-by-Step Solution

Answer

The correct choice is Option A $\left(b=-4\right)$.

Step 1. State the concept.

A counterexample to a statement is a case which makes the statement false.

Step 2. List the given data.

The given statement is “$2b<3b$”.

Step 3. Solve.

Solving the given statement,

$\begin{array}{l}2b<3b\\ 2b-2b<3b-2b\\ 0<b\\ b>0\end{array}$

 

So, the given statement is true for all $b>0$.

Step 4. Determine the counterexample.

Since a counterexample makes the statement false, it must be a value such that $b<0$.

 

Of the given options, the only value of $b$, for which $b<0$ is option A $\left(b=-4\right)$

 

So, the correct choice is Option A $\left(b=-4\right)$.