Problem 56 - Introductory Algebra for College Students

Question

Simplify each algebraic expression. $$-10 b+13+(-b)+(-4)$$

Step-by-Step Solution

Answer

The simplified form of the expression \(-10b + 13 + (-b) + (-4)\) is \(-11b + 9\).

Step 1: Combine Like Terms (Variables)

First, identify the terms that include the variable 'b'. There are two such terms: '-10b' and '(-b)'. To combine these terms, add or subtract them as indicated. Thus, when you combine '-10b' and '(-b)', you get \(-10b - b = -11b\). So the simplified version of these terms is \(-11b\).

Step 2: Combine Like Terms (Constants)

Next, look at the constants in the expression. There are two constant numbers: '13' and '(-4)'. Like the variable terms, these constants can be combined by performing the indicated arithmetic operation. When you add '13' and '(-4)' together, you get \(13 - 4 = 9\). So, the combined form of these constants is '9'.

Step 3: Write Final Simplified Expression

Having combined both the variable terms and the constant terms separately, you now put them together to get the final simplified form of the expression. Thus, the expression \(-10b + 13 + (-b) + (-4)\) simplifies to \(-11b + 9\).