Question

Using the systematic method solve the equation \[3(x - 2) = 15\].

Answer 1

Hint: To solve the equation of the form $ax = b$, we are required to divide both sides of the equation by $a$ to get the equation of the form $x = \dfrac{b}{a}$ ,and to solve the equation of the form $x - a = b$, we are required to add $a$ on both sides of the equation, to get the equation of the form $x = b + a$

Complete step-by-step solution:
The given equation is \[3(x - 2) = 15\].
We are required to solve the above equation using systematic steps.
We notice that this equation is of the form $ax = b$, so we are required to divide both sides of the equation by $a$ to get the equation of the form $x = \dfrac{b}{a}$.
In the above equation we get, $a = 3$
First, divide both sides of the equation by \[3\], we get
\[\dfrac{{[3(x - 2)]}}{3} = \dfrac{{15}}{3}\]
Simplify the above equation by cancelling $3$from the numerator and denominator on the left side of the equation.
\[(x - 2) = \dfrac{{15}}{3}\]
Reduce the fraction on the right-side terms of the above equation, to get
\[(x - 2) = 5\]
Now, the above equation is of the form $x - a = b$, we are required to add $a$ on both sides of the equation, to get the equation of the form $x - a + a = b + a$ , which can be further simplified as $x = b + a$ since $( - a + a) = 0$.
From the given equation we get $a = 2$.
Add the number $2$ on both sides of the above equation,
\[(x - 2) + 2 = 5 + 2\]
Write the number $ - 2$ in the form of $ + ( - 2)$ in the above equation,
$(x + ( - 2)) + 2 = 5 + 2$
Since \[x\] is also a real number, so by the associative property of addition: $(a + b) + c = a + (b + c)$, we can write
$(x + ( - 2)) + 2 = x + (( - 2) + 2)$
It can further be written as
$(x + ( - 2)) + 2 = x$
Substitute the above value in the equation $(x + ( - 2)) + 2 = 5 + 2$,
$x = 5 + 2 = 7$
Hence, the solution of the equation \[3(x - 2) = 15\] is $x = 7$.

Note: Equation of the form $ax - c = b$, can be written in the form of \[x = \dfrac{{b + c}}{a}\] by following a series of steps of adding $c$on both sides and dividing it by $a$.
Using the basic operations we solved the given problem.