How do you solve\[\left| 3-2r \right|=7\]?

Hint: In the given question, we have been asked to find the value of ‘r’ and it is given that \[\left| 3-2r \right|=7\]. This is the absolute value equation, in order to find the value of ‘r’ first we need to find two separate equations considering one side equal to the positive of the other side of the given equation and the second time, one side equals to the negative of the other side of the given equation. In this way we will get two equations and we need to solve each equation separately in a way we solve the general equation.

Complete step by step solution:
We have given the absolute value,
\[\left| 3-2r \right|=7\]
Removing the absolute bars, we get
\[\Rightarrow 3-2r=7\ and\ -\left( 3-2r \right)=7\]
Now, solving
\[\Rightarrow 3-2r=7\]
Subtracting 3 from both the sides of the equation, we get
\[\Rightarrow 3-2r-3=7-3\]
Simplifying the above, we get
\[\Rightarrow -2r=4\]
Dividing both the sides of the equation by -2, we get
\[\Rightarrow \dfrac{-2r}{-2}=\dfrac{4}{-2}\]
Simplifying the above, we get
\[\Rightarrow r=-2\]
Now, solving
\[\Rightarrow -\left( 3-2r \right)=7\]
Open the bracket in the above equation, we get
\[\Rightarrow -3+2r=7\]
Adding 3 to both the side of the equation, we get
\[\Rightarrow -3+2r+3=7+3\]
Simplifying the above, we get
\[\Rightarrow 2r=10\]
Dividing both the sides by 2, we get
\[\Rightarrow r=5\]
Thus, we get
\[\Rightarrow r=-2,5\]
Therefore, the possible values of ‘r’ are -2 and 5.

Note: In solving these types of questions, students should remember that when we remove modulus from the modulus function then we get two equations. One with a positive sign and the other with a negative sign. Always be sure when you transpose a term to the other side of the equation. The sign of the term always changes when it is moved to the one side of the equation to the other side of the equation.