Answer:
Explanation:
Given:
[tex](4x)^{\frac{1}{3}}\text{ - x = 0}[/tex]To find:
the steps in solving the expression and the value(s) of x
To determine the value of x, first, we will add x to both sides:
[tex]\begin{gathered} (4x)^{\frac{1}{3}}\text{ -x + x = 0 + x} \\ (4x)\placeholder{⬚}^{\frac{1}{3}}\text{ }=\text{ x} \end{gathered}[/tex]Next, cube both sides of the equation:
[tex]\begin{gathered} ((4x)^{\frac{1}{3}})^3\text{ = x}^3 \\ ((4x)^{\frac{3}{3}})^\text{ = x}^3 \\ 4x\text{ = x}^3 \end{gathered}[/tex]Lastly, solve for x to determine the number of solutions:
[tex]\begin{gathered} subtract\text{ 4x from both sides:} \\ x^3\text{ - 4x = 0} \\ x(x^2\text{ - 4\rparen = 0} \\ x\text{ = 0 or x}^2-4\text{ = 0} \\ \\ x^2\text{ - 4 = 0} \\ x^2\text{ = 4} \\ x\text{ = }\pm\sqrt{4} \\ x\text{ = }\pm2 \\ \\ The\text{ values of x = -2, 0, 2} \end{gathered}[/tex][tex][/tex]The first step in solving the equation is to add x to both sides. The second step is to cube both sides.
Solving this equation for x initially yields 3 possible solutions. Checking the solutions shows