Question

-5 + bx = 2x + 3(x + 2)
In the above equation, b is a constant. For what value of b does the equation have no solution?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C 5

First, we observe that this is a linear equation with one vairable. This linear equation will have no solutions if the equation reduces to an equation of the form $\text{px + q = rx + s}$,
where $\text{p = r}$ and $\text{q}\ne \text{s}$

Now, rewrite the equation in an equivalent form using the distributive property and combining like terms.

$\text{-5 + bx = 2x + 3(x + 2)}$

$⟹\text{-5 + bx = 2x + 3x + 6}$

$⟹\text{-5 + bx = 5x + 6}$

Since $-5$ $\ne$ 6, the equation will have no solution if b = 5.