Chapter 10: Chapter 10

Problem 192

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Solve the equation \((3 / 4) \mathrm{x}+(7 / 8)+1=0\)

Short Answer

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The solution to the equation \((\frac{3}{4})x + (\frac{7}{8}) + 1 = 0\) is \(x = -\frac{5}{2}\).

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Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Combine the constants

First, let's combine the constants \(\frac{7}{8}\) and \(1\). To do this, we need a common denominator. Since the denominator of the fraction \(\frac{7}{8}\) is already \(8\), we will convert \(1\) to a fraction with the same denominator: \(1 = \frac{8}{8}\). Now we can add the fractions: \(\frac{7}{8} + \frac{8}{8} = \frac{15}{8}\). The equation becomes: \((\frac{3}{4})x + \frac{15}{8} = 0\).

Step 2: Isolate the x term

Next, we need to isolate the x term, \((\frac{3}{4})x\), by moving \(\frac{15}{8}\) to the other side of the equation. We can do this by subtracting \(\frac{15}{8}\) from both sides: \[(\frac{3}{4})x + \frac{15}{8} - \frac{15}{8} = 0 - \frac{15}{8} \] This simplifies to: \[(\frac{3}{4})x = -\frac{15}{8}\]

Step 3: Solve for x

Now all that's left is to solve for x by dividing both sides of the equation by \(\frac{3}{4}\). To do this, we can instead multiply by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\): \[(\frac{3}{4})x \cdot \frac{4}{3} = -\frac{15}{8} \cdot \frac{4}{3}\] This simplifies to: \[x = -\frac{15}{8} \cdot \frac{4}{3}\]

Step 4: Simplify the equation

Now, let's simplify the equation to find the solution for x. To do this, we will multiply the fractions: \[-\frac{15}{8} \cdot \frac{4}{3} = -\frac{15 \times 4}{8 \times 3}\] This simplifies to: \[x = -\frac{60}{24}\]

Step 5: Reduce the fraction

Finally, we need to reduce the fraction \(-\frac{60}{24}\) to its simplest form. The greatest common divisor (GCD) of \(60\) and \(24\) is \(12\), so we can divide both the numerator and the denominator by \(12\): \[x = -\frac{60 \div 12}{24 \div 12}\] This simplifies to: \[x = -\frac{5}{2}\] So, the solution to the equation \((\frac{3}{4})x + (\frac{7}{8}) + 1 = 0\) is \(x = -\frac{5}{2}\).

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Chapter 10: Chapter 10

Solve the equation \((3 / 4) \mathrm{x}+(7 / 8)+1=0\)

Short Answer

Step by step solution

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Step 1: Combine the constants

Step 2: Isolate the x term

Step 3: Solve for x

Step 4: Simplify the equation

Step 5: Reduce the fraction

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