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Solve the following equation for \( \% \) \( 2=\sqrt[3]{4 x-12} \) a) 10 (b) 5 c) 3 c) 8

Ask by Ingram Knight. in the United States
Jan 26,2025

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Answer

\( x = 5 \)

Solution

To solve the equation for \( x \): \[ 2 = \sqrt[3]{4x - 12} \] **Step 1: Eliminate the Cube Root** Cube both sides of the equation to eliminate the cube root: \[ 2^3 = (\sqrt[3]{4x - 12})^3 \] \[ 8 = 4x - 12 \] **Step 2: Solve for \( x \)** Add 12 to both sides: \[ 8 + 12 = 4x \] \[ 20 = 4x \] Divide both sides by 4: \[ x = \frac{20}{4} = 5 \] **Answer:** **b) 5**

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The Deep Dive

To solve the equation \( 2 = \sqrt[3]{4x - 12} \), first, we cube both sides to eliminate the cube root: \[ 2^3 = 4x - 12 \] This simplifies to: \[ 8 = 4x - 12 \] Next, we add 12 to both sides: \[ 8 + 12 = 4x \] \[ 20 = 4x \] Now, divide by 4: \[ x = 5 \] So, the correct answer is (b) 5. Now, let's have a little fun with some interesting tidbits! Did you know that the cube root has been used in mathematics since ancient civilizations? The Babylonians had methods to approximate cube roots, paving the way for algebraic advancements. So next time you see a cube root, remember it has a long-standing history in shaping mathematical concepts! If you're tackling similar problems, a common mistake is forgetting to handle the exponent correctly when eliminating roots. Always double-check that you're performing the same operation across the equation, especially when it involves roots and exponents! Happy problem-solving!

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