Problem 7 Simplify the expression. $$5 z... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 7

Simplify the expression. $$5 z-8(z-3)-20$$

Short Answer

Expert verified

-3z + 4

Step by step solution

Distribute the -8

Distribute the -8 across the terms inside the parentheses: $-8(z - 3)$ becomes $-8z + 24$. The expression now looks like this: $5z - 8z + 24 - 20$.

Combine like terms

Combine the like terms for the variable $z$ and the constant terms. $5z - 8z = -3z$ and $24 - 20 = 4$. Now, the expression is $-3z + 4$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property

The distributive property is a fundamental concept in algebra that helps you to simplify expressions. It states that for any numbers (or variables) a, b, and c, the expression $a(b + c)$ can be expanded to $ab + ac$.
This property allows you to remove parentheses by distributing the multiplication across each term inside.

Example 1: In the expression $3(x + 2)$, distribute the 3 to both x and 2, resulting in $3x + 6$.
Example 2: For an expression like $-2(y - 5)$, distribute -2, giving $-2y + 10$.

Combining Like Terms

Combining like terms simplifies an expression by reducing it to fewer terms. Terms are 'like' if they have identical variables raised to the same power.
For instance:

$5z$ and $-8z$ are like terms because they both contain the variable z.
$24$ and $-20$ are like terms because they are both constants with no variables.

To combine like terms, you add or subtract their coefficients:

Combining $5z$ and $-8z$ results in $-3z$.
Adding $24$ and $-20$ gives $4$.

Therefore, the expression $5z - 8z + 24 - 20$ is simplified to $-3z + 4$.

Variables in Algebra

Variables are symbols (typically letters) representing unknown quantities in algebra. Common variables include x, y, and z. They allow mathematicians to construct general expressions and equations that can solve real-world problems.
Here鈥檚 what to remember about variables:

Variables can stand for different values; their purpose is to make the expression adaptable.
Operations with variables follow the same rules as those with numbers.
Combining variables with coefficients (like 5 in 5z) adjusts the value they represent.
Variables can also interact in very powerful ways. They can be multiplied, divided, added, or subtracted from each other.

This allows algebraic expressions to be both flexible and powerful. In the given problem, the variable is z, and it helps in forming terms like $5z$, $-8z$, and eventually $-3z$.

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91影视

Simplify the expression. $$5 z-8(z-3)-20$$

Short Answer

Step by step solution

Distribute the -8

Combine like terms

Key Concepts

Distributive Property

Combining Like Terms

Variables in Algebra

One App. One Place for Learning.

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