To solve the expression \( 2x - 30 - \frac{2}{5}x + 5 \), we will combine like terms. Let's go through the steps:

### Step 1: Combine like terms
1. Group the terms with \( x \) together: \( 2x \) and \( -\frac{2}{5}x \).
2. Group the constant terms together: \( -30 \) and \( +5 \).

### Step 2: Combine the \( x \) terms
- To combine \( 2x \) and \( -\frac{2}{5}x \), we first need a common denominator.
- The common denominator for 1 and 5 is 5.

\[
2x = \frac{10}{5}x \quad \text{(since \( 2 = \frac{10}{5} \))}
\]

Now, subtract \( \frac{2}{5}x \) from \( \frac{10}{5}x \):

\[
\frac{10}{5}x - \frac{2}{5}x = \frac{8}{5}x
\]

### Step 3: Combine the constant terms
\[
-30 + 5 = -25
\]

### Step 4: Write the simplified expression
Now, substitute the simplified terms back into the expression:

\[
\frac{8}{5}x - 25
\]

This is the simplified form of the given expression.

### Do you want details or have any questions?

### Related Questions:

1. How would you solve the equation if it was \( 2x - 30 - \frac{2}{5}x + 5 = 0 \)?
2. How can you convert the expression \( \frac{8}{5}x - 25 \) to a decimal form?
3. What steps would you follow to solve \( 2x - 30 - \frac{1}{3}x + 5 \)?
4. How do you handle like terms with different coefficients and variables?
5. What are the applications of combining like terms in solving algebraic equations?

### Tip:

Always look for like terms in an algebraic expression. Combining them simplifies the expression, making it easier to solve or manipulate further.

Learn how to simplify the algebraic expression 2x - 30 - 2/5x + 5 step-by-step. This problem involves combining like terms and applying basic arithmetic operations. Suitable for students in Grades 7-9.

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