https://file.aiquickdraw.com/mathbot/file/17261840999549f7bu624.jpg

Let's solve the equation shown in the image step by step:

\[
\frac{3}{10}x - \frac{2}{5} = -1
\]

### Step 1: Eliminate the fractions
To eliminate the fractions, find the least common denominator (LCD) of \(10\) and \(5\), which is \(10\). Multiply the entire equation by \(10\):

\[
10 \times \left( \frac{3}{10}x \right) - 10 \times \left( \frac{2}{5} \right) = 10 \times (-1)
\]

This simplifies to:

\[
3x - 4 = -10
\]

### Step 2: Solve for \(x\)
Now, solve the simplified equation:

\[
3x - 4 = -10
\]

Add \(4\) to both sides:

\[
3x = -10 + 4
\]

\[
3x = -6
\]

Now, divide both sides by \(3\) to isolate \(x\):

\[
x = \frac{-6}{3}
\]

\[
x = -2
\]

Thus, the solution is:

\[
x = -2
\]

Let me know if you'd like more details or have any further questions!

Here are five related questions to consider:
1. How do you solve an equation with variables on both sides?
2. What is the least common denominator, and how is it found?
3. How do you solve a system of equations with fractions?
4. How can you check if a solution to an equation is correct?
5. What happens if an equation has no solution or infinite solutions?

**Tip:** Always try to eliminate fractions early when solving equations to make the process simpler.

Solve the equation for x: (3/10)x - 2/5 = -1

Learn how to solve the linear equation (3/10)x - 2/5 = -1. This step-by-step solution covers eliminating fractions, isolating the variable, and simplifying the equation. Suitable for students in Grades 7-8.

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