Question

Solve the following equation and check the result
A. $ 3x = 2x + 18 $
B. $ 5t - 3 = 3t - 5 $
C. $ 4z + 3 = 6 + 2z $
D. $ 2i - 1 = 14 - i $

Answer 1

Hint: In order to solve this question we will first take this equation as the starting point then we will take all the constant to one side then and similarly all the variables to the other side and then add or subtract it according to the sign convention given in the question and we will go to the final result.

Complete step by step solution:
For solving this question we will go for one by one option and we will solve it one by one:
In this question the basic equation given to us is:
I. $ 3x = 2x + 18 $
For solving this we will take all the variables to one side and all the constants to other side we will get:
 $ 3x - 2x = 18 $
Now on further solving this we will get:
 $ x = 18 $
Now as it is stated in question that we have to check it so we will be putting the value of x in the main equation:
 $ 3 \times 18 = 2 \times 18 + 18 $
On further solving this we will get:
 $ 54 = 54 $
Since right and left hand sides are equal so it is proved that this value is correct.

In this question the basic equation given to us is:
II. $ 5t - 3 = 3t - 5 $
For solving this we will take all the variables to one side and all the constants to other side we will get:
 $ 5t - 3t = - 5 + 3 $
Now on further solving this we will get:
 $ t = - 1 $
Now as it is stated in question that we have to check it so we will be putting the value of x in the main equation:
 $ 5\left( { - 1} \right) - 3 = 3\left( { - 1} \right) - 5 $
On further solving this we will get:
 $ - 8 = - 8 $
Since right and left hand sides are equal so it is proved that this value is correct.

In this question the basic equation given to us is:
III. $ 4z + 3 = 6 + 2z $
For solving this we will take all the variables to one side and all the constants to other side we will get:
 $ 4z - 2z = 6 - 3 $
Now on further solving this we will get:
 $ z = \dfrac{3}{2} $
Now as it is stated in question that we have to check it so we will be putting the value of x in the main equation:
 $ 4 \times \dfrac{3}{2} + 3 = 6 + 2 \times \dfrac{3}{2} $
On further solving this we will get:
 $ 9 = 9 $
Since right and left hand sides are equal so it is proved that this value is correct.

In this question the basic equation given to us is:
IV. $ 2i - 1 = 14 - i $
For solving this we will take all the variables to one side and all the constants to other side we will get:
 $ 2i + i = 14 + 1 $
Now on further solving this we will get:
 $ i = 5 $
Now as it is stated in question that we have to check it so we will be putting the value of x in the main equation:
 $ 2 \times 5 - 1 = 14 - 5 $
On further solving this we will get:
 $ 9 = 9 $
Since right and left hand sides are equal so it is proved that this value is correct.

Note: While solving these types of questions we should keep in mind that we should make the correct transformations of the constants and variables it is because if the transformation is made wrong or its sign is written wrong the answer will be coming incorrect.