I am having an extremely tough time with integers in algebra when simplifying algebraic expressions. No matter which method I use I still end up confused and end up with a completely different answer.

Ex:

5t-{7t-[4r-3(t-7)]+6r}-4r

Simplifying algebraic expressions involving integers can be tricky at first, but with practice and understanding of a few key rules, you can become more comfortable with it. Let me guide you through the steps to simplify the expression you provided.

First, let's break down the expression into smaller parts and simplify them one by one:

5t - {7t - [4r - 3(t - 7)] + 6r} - 4r

Step 1: Simplify the innermost parentheses
Inside the innermost parentheses, you have (t - 7). To simplify this expression, you distribute the -3 to both terms inside the parentheses:

= 5t - {7t - [4r - 3t + 21] + 6r} - 4r

= 5t - {7t - 4r + 3t - 21 + 6r} - 4r

Step 2: Combine like terms within the innermost parentheses
Inside the innermost parentheses, you have several terms with similar variables. Combine them together:

= 5t - {10t + 2r - 21} - 4r

Step 3: Remove the outermost set of parentheses
Now, remove the outermost set of parentheses. To do this, distribute the negative sign that's in front of the curly braces to all the terms inside:

= 5t - 10t - 2r + 21 - 4r

Step 4: Combine like terms outside the parentheses
Combine the like terms together:

= (5t - 10t) + (-2r - 4r) + 21

= -5t - 6r + 21

So the simplified expression is -5t - 6r + 21.

To check your answer, you can substitute values for t and r and compare the results using both the original expression and your simplified version. Remember to double-check your calculations and be careful with signs when dealing with negatives.

With practice, you'll become more comfortable and confident in simplifying algebraic expressions involving integers.