What is the solution to this equation?
[tex]\sqrt[3]{\left(\frac{1}{8}-x\right)}=-\frac{1}{2}[/tex]
The solution is $\square$.
Answer (2)
Cube both sides of the equation: ( 3 ( 8 1 − x ) ) 3 = ( − 2 1 ) 3 .
Simplify the equation: 8 1 − x = − 8 1 .
Isolate x: x = 8 1 + 8 1 .
Simplify to find the value of x: x = 4 1 . The solution is 4 1 .
Explanation
Understanding the Problem We are given the equation 3 ( 8 1 − x ) = − 2 1 . Our goal is to find the value of x that satisfies this equation.
Cubing Both Sides To eliminate the cube root, we cube both sides of the equation: ( 3 ( 8 1 − x ) ) 3 = ( − 2 1 ) 3
Simplifying the Equation Simplifying the equation, we have: 8 1 − x = − 8 1
Isolating x To isolate x , we add x and 8 1 to both sides of the equation: 8 1 + 8 1 = x
Finding the Value of x Simplifying the left side, we find the value of x : x = 4 1
Final Answer Therefore, the solution to the equation is x = 4 1 .
Examples
Imagine you're baking a cake and need to adjust a recipe. If the original recipe calls for a certain amount of liquid, but you want to reduce the overall size of the cake, you might encounter an equation similar to this one. Solving for x helps you determine the exact amount of adjustment needed to maintain the correct proportions and achieve the desired outcome. This type of algebraic manipulation is essential for precise measurements and consistent results in cooking and baking.
The solution to the equation 3 ( 8 1 − x ) = − 2 1 is obtained by cubing both sides, simplifying, isolating x , and calculating the value. Therefore, x = 4 1 .
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