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Chapter 10: Chapter 10

Problem 189

Next question

Solve for \(x: 7 x-3=2(x+3)\)

Short Answer

Expert verified
The short answer for solving the equation \(7x - 3 = 2(x + 3)\) is: \(x = \frac{9}{5}\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Simplify both sides of the equation

Expand the expression on the right side of the equation by distributing the 2 to both terms inside the parentheses. This gives: \(7x - 3 = 2(x + 3)\) \(7x - 3 = 2x + 6\)

Step 2: Get all x terms on one side and constant terms on the other side

We'll move the x terms to the left side by subtracting 2x from both sides. This will cancel out x terms on the right side. Also, we'll move the constant terms to the right side by adding 3 to both sides. This will cancel out the constant terms on the left side. \(7x - 2x - 3 + 3 = 2x - 2x + 6 + 3\) \(5x = 9\)

Step 3: Solve for x by dividing by the coefficient

Now, we need to isolate x by dividing both sides of the equation by the coefficient of x, which is 5. \(5x / 5 = 9 / 5\) \(x = \frac{9}{5}\) So, the solution for x is \(x = \frac{9}{5}\).

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