Problem 54
Question
Simplify each algebraic expression. $$5 y+(-11 z)+(-15 y)+20 z$$
Step-by-Step Solution
Verified Answer
The simplified form of the given algebraic expression is \(-10y + 9z\).
1Step 1: 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'.
2Step 2: 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.
3Step 3: 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.
4Step 4: Final Simplified Expression
The final simplified expression would be the combination of the simplified 'y' and 'z' terms. Thus, the simplified expression is \(-10y + 9z\).
Other exercises in this chapter
Problem 54
Insert either \(\) in the shaded area between each pair of numbers to make a true statement. $$0 \square-\frac{1}{2}$$
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Determine whether the given number is a solution of the equation. $$5 a-3=2 a+6 ; 3$$
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Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{8} \div \frac{2}{3}$$
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Simplify each series of additions and subtractions. $$-6-2+3-10$$
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