Question

How do you solve 5(a – 1) – 15 = 3(a + 12) + 4?

Answer 1

Hint: In this problem, we are given a linear equation in one variable and that unknown variable is ‘a’ which we have to find out in this particular question. We are given two sides of the equation, which are to be simplified individually first. There is a need for simplification so that it becomes easy to find the value of ‘a’.

Complete step-by-step answer:
Now, let’s discuss all the steps for simplification but before that let’s understand the concept of linear equation. Linear equation is basically an equation in which there is one or more than one unknown variable. For example: 2x + 4 = 5, 6x – 3y = 9 etc. When we say the word linear, it means straight. So it is that equation which gives us a straight line when it is plotted on the graph. For this particular question, we are given a linear equation in one variable. And this variable is unknown whose value needs to be found out.
Write the equation now.
$\Rightarrow $5(a – 1) – 15 = 3(a + 12) + 4
First, open the brackets:
$\Rightarrow $5a – 5 – 15 = 3a + 36 + 4
Keep all the variables containing terms on the left hand side and constant terms on the right hand side.
$\Rightarrow $5a – 3a = 36 + 4 + 15 + 5
Further, do all the calculations:
$\Rightarrow $2a = 60
As we can see, 2 is in multiplication with ‘a’, when it will be taken to other side it will get divide:
$\Rightarrow $a = $\dfrac{60}{2}$
Reduce the terms now:
$\therefore $a = 30
This is the final answer.

Note: When we plot this line on a graph, there also it will give us the same value for ‘a’. If you want to verify the answer whether it is correct or not, all you can do is plot or check by putting the obtained value directly into the equation given. If that value satisfies the equation that means the value of ‘a’ is correct.