Solve the following equation for x. ¹⁄₃ (12x - 3)² = 27

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When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. ¹⁄₃ (12x - 3)² = 27 The first step is to eliminate the ¹⁄₃ on the left side of the equation. We do this by multiplying both sides of the equation by 3. (Remember that when dividing by a fraction, you multiply the reciprocal. In this case, the reciprocal of ¹⁄₃is ³⁄₁ which is equal to 3.) ¹⁄₃ (12x - 3)² = 27 ¹⁄₃ (12x - 3)² × 3 = 27 × 3 (12x - 3)² = 81 Now we need to eliminate the exponent on the left side of the equation. We do this by taking the square root of each side. √(12x - 3)² = √81 12x - 3 = √81 Since the square root of 81 is both 9 and -9, we must solve for both. 12x - 3 = √81 12x - 3 = ±9 11ec0fb7_2745_2ff7_95f0_99cb8b7ccc91_NR0002_00

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