Chapter 10: Chapter 10

Problem 188

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Solve for \(x: 2 x+5 x=7-x\)

Short Answer

Expert verified

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

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Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Combine like terms on both sides of the equation

Combine the \(x\) terms on both sides of the equation. On the left side, we have \(2x + 5x\), and on the right side, we have \(7 - x\).

Step 2: Add \(x\) to both sides

First, we need to isolate \(x\). We do this by adding \(x\) to both sides of the equation: \[ (2x + 5x) + x = 7 - x + x \]

Step 3: Simplify both sides

Now, we can add the \(x\) terms on both sides of the equation. On the left side, we have \(2x + 5x + x = 8x\), and on the right side, we have \(7 - x + x = 7\): \[ 8x = 7 \]

Step 4: Isolate \(x\)

Now we need to isolate \(x\). To do this, we will divide both sides of the equation by \(8\): \[ \frac{8x}{8} = \frac{7}{8} \]

Step 5: Solve for \(x\)

Finally, we can finish solving the equation. Since \(\frac{8x}{8}\) is simply \(x\), we find that: \[ x = \frac{7}{8} \] So the solution to the equation \(2x + 5x = 7 - x\) is \(x = \frac{7}{8}\).

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Chapter 10: Chapter 10

Solve for \(x: 2 x+5 x=7-x\)

Short Answer

Step by step solution

Unlock all solutions

Step 1: Combine like terms on both sides of the equation

Step 2: Add \(x\) to both sides

Step 3: Simplify both sides

Step 4: Isolate \(x\)

Step 5: Solve for \(x\)

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