If you are looking for different ways via which you could solve for x, then you are welcome here. The content is meant for those students who face problems while solving radicals and exponents in algebra. After reading this content, you will get the right method to solve it. So, let’s start this learning session.
Basic linear equation
We are going to solve simple linear equation 5x – 8 = x + 4 and find out the value of X.
Step 1: At first, we will arrange 5x and x on the left-hand side and 4 and on the right-hand side.
5x – 8 = x + 4
Step 2: After that, we will solve the arrange number and here is the further procedure:
Important note: Before solving any equation, students should solve exponents if there is any to make the equation easy.
Solve it by isolating the terms (in case of exponents)
If you didn’t get it as what I meant by the word “isolating” then here is an explanation for you. It means that you should make one term disappear to get the value of X. The trick is quite popular plus makes the procedure easy. So, how to solve for x by this method?
Example: 2x² + 14 = 46
Step 1: In the above example, we are going to isolate term 14 and thus we ill subtract both the sides by 14. Keep in mind that you should choose an opposite side for isolating a term, i.e., here 14 is positive and thus we have chosen (-14) in it.
2x² + 14 – 14 = 46 – 14
2x² = 32
Step 2: Now you see that number 14 has gone and now we can find the value of x easily. Here are its further steps:
Now, we know that 16 is the square of 4 and thus we will square root both the sides and get:
x = 4
Solving fractions by cross multiplication method
Fractions are easy to solve, by using multiplication methods we can get the value of X. So, here is the example:
Step 1: We will solve this by cross multiplication method where we will multiply 4) by 4 and 3 by 4.
(x – 4) (4) = (2) (4)
4x – 16 = 8
Step 2: Now we will combine the like terms like this:
4x = 8 + 16
4x = 24
X = 24 ⁄ 4
And finally, we get x = 6. The cross multiplication method is very easy but does not forget to reduce the problem into simplest form.
Solve for x using radical signs
For this one, you need to learn some basic concepts of radical sign or square roots. Now, let’s solve example
Step 1: In the first step, we will isolate the number 5 by adding 5 on both the sides like this:
Step 2: Now we are going to square both the sides:
Step 3: Again, we will subtract both the sides by 7 so that 2x remain on the LHS:
So, we have got the answer 9, and you can verify this answer by putting the value of x in the problem.
Hope so all the methods explained above let you solve for x easily and make your mathematics stronger.