Question

If \[\sqrt[3]{{2x + 4}} = - 0.375\], then \[x = \]
A) \[ - 2.03\]
B) \[ - 1.97\]
C) \[ - 0.87\]
D) \[ - 0.34\]
E) \[1.43\]

Answer 1

Hint:
Here we will use the concept of cube root to simplify the equation. Firstly we will remove the cube root from the equation by finding the cube of terms present on both sides of the equation. Then we have to solve the equation to get the value of \[x\].

Complete step by step solution:
Now we have to solve the equation to get the value of \[x\].
Here in the given equation, one side of the equation has the cube root of an expression. So to remove the cube root we will cube terms on both sides of the equation.
We will first find the cubes of terms on both the sides of the equation.
\[{\left( {\sqrt[3]{{2x + 4}}} \right)^3} = {\left( { - 0.375} \right)^3}\]
\[ \Rightarrow 2x + 4 = 52.73 \times {10^{ - 3}}\]
The value on the right side of the term is very small that is why we took the value in the multiple of 10. Now we will solve the above equation to get the value of the \[x\].
Subtracting 4 from both side, we get
\[\begin{array}{l} \Rightarrow 2x = 52.73 \times {10^{ - 3}} - 4\\ \Rightarrow 2x = - 3.94\end{array}\]
Dividing both side by 2, we get
\[ \Rightarrow x = \dfrac{{ - 3.94}}{2}\]
\[ \Rightarrow x = - 1.97\]
Hence, the value of \[x\] is \[ - 1.97\].

So, option B is the correct option.

Note:
Here we removed the cube root by finding the cube of the terms. The cube root of a number is the factor that we multiply by itself three times to get the original number. We should not confuse the cube root with the square root. The square root of a number is the factor that we multiply by itself two times to get that number.
Square root is expressed as \[\sqrt[2]{{{\rm{number}}}}\], whereas cube root is expressed as \[\sqrt[3]{{{\rm{number}}}}\].