The expression \( a + 2b \) is greater than \( b - a \) by:

\[
(a + 2b) - (b - a)
\]

First, distribute the negative sign:

\[
a + 2b - b + a
\]

Combine like terms:

\[
2a + b
\]

So, \( a + 2b \) is \( 2a + b \) greater than \( b - a \).

Would you like a more detailed explanation or have any questions?

### Related Questions:
1. If \( a = 3 \) and \( b = 2 \), what is the value of \( 2a + b \)?
2. How would the expression change if both \( a \) and \( b \) are negative?
3. What happens to the difference \( 2a + b \) if \( a \) is doubled?
4. If \( a = b \), what is the resulting difference between \( a + 2b \) and \( b - a \)?
5. How would the difference change if you add a constant \( c \) to both \( a + 2b \) and \( b - a \)?

### Tip:
Always remember to carefully distribute negative signs when subtracting expressions.

Explore the solution to the algebraic inequality problem: how much is a + 2b greater than b - a? This problem involves understanding inequalities in algebra, with a step-by-step explanation and example scenarios. Suitable for students in Grades 7-9.

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