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Problem 189

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

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