Question

Solve the following linear equations
a. $x - 5 = 7$
b. $3x + 14 = 48$
c. $2x = 48$
d. $5(x - 1) + 3 = 23$

Answer 1

Hint: Linear equations can be defined as the equations with unknown variables present in it, with the degree of 1. If the above example is considered, that is a linear equation with just one variable, the steps are very simple and there can be different ways in which the question can be solved. Basic methods of addition, subtraction and multiplication are only used. We get the value of x by bringing all the terms of x to one side and keeping the rest on the other.

Complete step by step answer:
Equation given in the question:
a. $x - 5 = 7$
To find: x
As we want the value of x, we take all other values to one side.
Therefore, taking 5 on other side, we get,
$x = 7 + 5 = 12$
Therefore, $x = 12$
b. $3x + 14 = 48$
To find: x
As we want the value of x, we take all other values to one side.
Therefore, taking 14 on other side and then dividing by 3 on both sides, we get,
$x = \dfrac{{48 - 14}}{3} = \dfrac{{34}}{3}$
Therefore, $x = \dfrac{{34}}{3}$
c. $2x = 48$
To find: x
As we want the value of x, we take all other values to one side.
Therefore, dividing by 2 on both sides, we get,
$x = \dfrac{{48}}{2} = 24$
Therefore, $x = 24$
d. $5(x - 1) + 3 = 23$
To find: x
As we want the value of x, we take all other values to one side.
Therefore, taking 3 on other side and then dividing by 5 on both sides, we get,
$x - 1 = \dfrac{{23 - 3}}{5}$
Taking 1 on other side, we get,
$x = \dfrac{{20}}{5} + 1 = 4 + 1 = 5$
Therefore, $x = 5$

Note:
Addition, subtraction, all these methods are to be performed correctly, most of the mistakes happen because of the wrong sign. Just to be sure about your answer, you can put the value of x in the original equation and compare.