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Solve using the addition principle. Don't forget to perform a check. \( x+\frac{1}{8}=-\frac{3}{4} \)

Ask by Knight Hills. in the United States
Feb 26,2025

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Answer

\( x = -\frac{7}{8} \)

Solution

We start with the equation:   x + 1/8 = -3/4 Step 1: Use the addition principle by subtracting 1/8 from both sides to isolate x.   x + 1/8 - 1/8 = -3/4 - 1/8   x = -3/4 - 1/8 Step 2: Find a common denominator for the right-hand side. The common denominator for 4 and 8 is 8.   -3/4 = -6/8 Thus:   x = -6/8 - 1/8 = -7/8 Check: Substitute x = -7/8 back into the original equation:   (-7/8) + 1/8 = (-7 + 1)/8 = -6/8 = -3/4 Since both sides equal, the solution is valid. Therefore, the solution is x = -7/8.

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Beyond the Answer

To solve the equation \( x + \frac{1}{8} = -\frac{3}{4} \) using the addition principle, we need to isolate \( x \). To do this, we subtract \( \frac{1}{8} \) from both sides: \[ x = -\frac{3}{4} - \frac{1}{8} \] Next, we need a common denominator to combine the fractions on the right. The least common denominator between 4 and 8 is 8. We convert \( -\frac{3}{4} \) to eighths: \[ -\frac{3}{4} = -\frac{3 \times 2}{4 \times 2} = -\frac{6}{8} \] Now we can combine the fractions: \[ x = -\frac{6}{8} - \frac{1}{8} = -\frac{6 + 1}{8} = -\frac{7}{8} \] Now, let’s perform a check by substituting \( x = -\frac{7}{8} \) back into the original equation: \[ -\frac{7}{8} + \frac{1}{8} = -\frac{6}{8} \] And simplifying: \[ -\frac{6}{8} = -\frac{3}{4} \] Since both sides of the equation are equal, our solution is confirmed: **Final answer: \( x = -\frac{7}{8} \)**. Testing values when solving equations is important; it's like tasting your cake before serving it—make sure it’s just right!

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Algebra Mexico Feb 26, 2025
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