https://file.aiquickdraw.com/mathbot/file/1726692174559blzyux1p.jpg

The equation displayed in the image is:

\[
\frac{2(x + 2)}{3} = 5x - 3
\]

### Let's solve this step by step:

1. **Clear the fraction**: Multiply both sides of the equation by 3 to eliminate the denominator.

\[
2(x + 2) = 3(5x - 3)
\]

2. **Distribute**: Distribute the constants on both sides.

\[
2x + 4 = 15x - 9
\]

3. **Move the variables to one side**: Subtract \(2x\) from both sides to move all \(x\)-terms to one side.

\[
4 = 13x - 9
\]

4. **Isolate the variable**: Add 9 to both sides.

\[
13 = 13x
\]

5. **Solve for \(x\)**: Divide both sides by 13.

\[
x = 1
\]

### Solution:
\[
x = 1
\]

Would you like more details, or do you have any questions about the steps?

Here are some related questions:
1. How do you check the solution by substituting \(x = 1\) back into the original equation?
2. Can this type of problem be solved graphically?
3. What are the rules for clearing fractions in algebraic equations?
4. How does distribution work in algebra?
5. Can equations with higher powers of \(x\) be solved similarly?

**Tip**: Always check your solution by substituting it back into the original equation to ensure no errors were made in the steps.

Solve the equation: (2(x + 2))/3 = 5x - 3

Learn how to solve the linear equation (2(x + 2))/3 = 5x - 3 using fraction clearing and distribution techniques. This step-by-step solution covers algebraic concepts and helps students understand how to isolate variables and check solutions. Ideal for students in Grades 8-10.

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