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Chapter 1: Problem 54

Simplify each algebraic expression. $$5 y+(-11 z)+(-15 y)+20 z$$

Short Answer

Expert verified
The simplified form of the given algebraic expression is \(-10y + 9z\).

Step by step solution

01

Identify Like Terms

In the expression \(5y+(-11z)+(-15y)+20z\), the like terms are terms that have the same variable, which are \(5y\) and \(-15y\) for variable 'y' and \(-11z\) and \(20z\) for variable 'z'.
02

Combine Like Terms - Variable y

Combine the 'y' terms: \(5y + (-15y) = -10y\). You add the coefficient of the 'y' terms which are 5 and -15, resulting in -10.
03

Combine Like Terms - Variable z

Combine the 'z' terms: \(-11z + 20z = 9z\). You add the coefficient of the 'z' terms which are -11 and 20, resulting in 9.
04

Final Simplified Expression

The final simplified expression would be the combination of the simplified 'y' and 'z' terms. Thus, the simplified expression is \(-10y + 9z\).

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