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Answer
\( x=60 \)
Solution
Solve the equation \( 6(x+4)^{\frac{1}{3}}-24=0 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(6\left(x+4\right)^{\frac{1}{3}}-24=0\)
- step1: Move the expression to the right side:
\(6\left(x+4\right)^{\frac{1}{3}}=24\)
- step2: Rewrite the expression:
\(\left(x+4\right)^{\frac{1}{3}}=4\)
- step3: Simplify the equation:
\(\left(\left(x+4\right)^{\frac{1}{3}}\right)^{3}=4^{3}\)
- step4: Evaluate:
\(x+4=64\)
- step5: Move the constant to the right side:
\(x=64-4\)
- step6: Subtract the numbers:
\(x=60\)
The solution to the equation \(6(x+4)^{\frac{1}{3}}-24=0\) is \(x=60\).
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Simplify this solution Mind Expander
To solve the equation \( 6(x+4)^{\frac{1}{3}}-24=0 \), let's start by isolating the cubic root term. First, add 24 to both sides: \[ 6(x+4)^{\frac{1}{3}} = 24 \] Next, divide both sides by 6: \[ (x+4)^{\frac{1}{3}} = 4 \] Now, to eliminate the cube root, cube both sides: \[ x + 4 = 4^3 \] \[ x + 4 = 64 \] Finally, subtract 4 from both sides to solve for \( x \): \[ x = 64 - 4 \] \[ x = 60 \] The solution is \( x = 60 \).
