Question

How do you solve $ 41 > 6m - 7? $

Answer 1

Hint: Here we are given greater than inequality pattern and so first of all we will clear the absolute value and accordingly follow the less than pattern. Will simplify the equations using the basic concepts and will find the value for the unknown term “m”.

Complete step by step solution:
Take the given expression: $ 41 > 6m - 7 $
Add on both the sides of the equation.
$ 41 + 7 > 6m - 7 + 7 $
Simplify the above equation finding the addition for the expression on the left hand side and also like terms with the same value and the opposite sign cancels each other.
$ 48 > 6m $
Divide the above expression with the number on both the sides of the expression.
$ \dfrac{{48}}{6} > \dfrac{{6m}}{6} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator on the right hand side of the expression.
$ \dfrac{{48}}{6} > m $
Find the factors for the term on the left hand side of the equation.
$ \dfrac{{6 \times 8}}{6} > m $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator on the left hand side of the expression.
$ 8 > m $ OR $ m < 8$
This is the required solution.
So, the correct answer is “ $ 8 > m $ or $ m < 8$”.

Note: Always remember when you add /subtract /multiply /divide any number on one side of the equation, its value gets changed so for the equivalent value you always have to perform any changes similar on both sides of the equation to keep the equivalent value of the original equation. Also, remember you can do addition and subtraction of the same value on one side as addition and subtraction of the same value cancel each other and ultimately value remains the same. The same way multiplication and division of the same number cancels each other.