Question

Consider the equation ax + 6 = 2(x + 3). For what values(s) of $a$does the equation have all the numbers as a solution? For what values(S) of $a$does the equation have just one solution?

Short answer

The value of $a$ is 2.

Step-by-step solution

Step-1 – Given

The given equation is $ax+6=2\left(x+3\right)$.

Step-2 – To determine

We have to find the value of $a$.

Step-3 – Calculation

Given equation: $ax+6=2\left(x+3\right)$

Using the distributive property:

$\Rightarrow ax+6=2x+6$

Subtract 6 from both sides,

$\Rightarrow ax+6-6=2x+6-6$

Simplify,

$ax=2x$

Divide both side of the equation by x;

$\Rightarrow \frac{ax}{x}=\frac{2x}{x}$

$\Rightarrow a=2$

So, the value of $a$is 2.