Question

How do you solve $ 3b - 6 \geqslant 15 + 24b $ ?

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 greater than pattern. Will simplify the equations using the basic concepts and will find the value for the unknown term “b”.

Complete step-by-step answer:
Take the given expression: $ 3b - 6 \geqslant 15 + 24b $
Subtract on both the sides of the equation.
 $ 3b - 6 - 3b \geqslant 15 + 24b - 3b $
Simplify the above equation considering that the like terms with the same value and the opposite sign cancels each other.
 $ - 6 \geqslant 15 + 21b $
Now, subtract with the number on both the sides of the equation.
 $ - 6 - 15 \geqslant 15 + 21b - 15 $
When you add two negative terms, you have to add and give negative sign to the resultant value.
 $ - 21 \geqslant 21b $
Divide both the sides of the above expression by
 $ - \dfrac{{21}}{{21}} \geqslant \dfrac{{21}}{{21}}b $
Common factors from the numerator and the denominator cancels each other. Therefore remove from the numerator and the denominator on the right hand side of the expression.
 $ - 1 \geqslant b $
This is the required solution.
So, the correct answer is “ $ - 1 \geqslant b $ ”.

Note: Always remember when you add /subtract /multiply /divide any number on one side of the equation, its value gets changes so for the equivalent value you always have to perform any changes similar on both the 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.