Question

How do you solve the equation: $6{h^2} = 3h?$

Answer 1

Hint: Here we are given an expression in the form of absolute value and is given in the modulus so the values can be plus or minus of “x”. So, here we will frame two equations using the same concepts and will find the value for “x”.

Complete step-by-step solution:
Take the given expression: $6{h^2} = 3h$
Take the term from the right hand side of the equation to the left hand side of the equation. When you move any term from one side to another, the sign of the term also changes. Positive terms become negative and vice-versa.
$6{h^2} - 3h = 0$
Take the common multiple common from both the terms in the above equation.
$3h(2h - 1) = 0$
$ \Rightarrow 3h = 0$ or $ \Rightarrow 2h - 1 = 0$
Case (I) $3h = 0$
When the term multiplicative on one side is moved to the opposite side, then it goes to the denominator.
$ \Rightarrow h = \dfrac{0}{3}$
Any number upon zero is always zero.
$ \Rightarrow h = 0$
Case (II) $2h - 1 = 0$
Move constant from left to the right hand side of the equation. When you move any term from one side to another then the sign of the term also changes. Negative terms become positive and vice-versa.
$2h = 1$
When the term multiplicative on one side is moved to the opposite side, then it goes to the denominator.
$ \Rightarrow h = \dfrac{1}{2}$
Hence, we get $h = 0$or $h = \dfrac{1}{2}$

Note: Be careful about the sign convention while simplification of the terms. Always remember when you move any term from one side to another, then the sign of the term also changes. Positive term becomes the negative term and the negative term becomes the positive term. Always remember zero multiplied with any number gives zero as the value and any number upon zero gives zero as the value.