/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 31 Simplify each expression. SEE EX... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 31

Simplify each expression. SEE EXAMPLE \(2 .\) (OB]ECTIVE 1 ) $$5(z-3)+2 z$$

Short Answer

Expert verified
The simplified form of the expression is \(7z - 15\).

Step by step solution

01

Distribute Multiplication over Subtraction

Start by distributing the multiplication operation over the subtraction operation inside the parentheses. Multiplying each term inside the parentheses by 5, which results in \(5z - 15\). So now, the expression becomes \(5z - 15 + 2z\).
02

Combine Like Terms

The next step is to group the like terms for simplification. In this expression, the like terms are \(5z\) and \(2z\). Adding these two gives \(7z\). The -15 carries down. The simplified expression becomes \(7z - 15\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Distributive Property
Understanding the distributive property is essential when beginning algebra. It's like sharing a bag of treats equally among your friends; each one gets an equal share. In algebra, the distributive property lets you multiply a single term by each term inside a parenthesis.

For example, with the expression $$5(z - 3)$$, we distribute 5 to both z and -3. Imagine that 5 is giving 1 bunch of itself to 'z' and 1 bunch to '-3'. After distributing, we get $$5z - 15$$. This move simplifies the expression and sets the stage for further simplification.
Combine Like Terms
Once we've distributed correctly, the next step is like cleaning up: combining what's similar. Think of it as grouping all the red socks together and all the blue socks separately in your drawer. In algebra, terms are 'like' if they have the same variables raised to the same power.

In our example after distributing, we get: $$5z - 15 + 2z$$. Here, $$5z$$ and $$2z$$ are like terms because both contain the variable z to the first power. We add them up, just like adding 5 apples to 2 apples, to get $$7z$$. The rest of the expression doesn't change, so we carry down the -15, leading to a final simplified expression of $$7z - 15$$.
Algebraic Simplification
Algebraic simplification is like tidying up a messy room so that you can find your stuff more easily; it makes the expression more workable. It involves distributing, combining like terms, and sometimes factoring. Your goal is to make the expression as straightforward as possible.

A useful tip is to always simplify step by step, checking your work as you go. Simplifying the example expression $$5(z-3)+2z$$, we followed these steps and found that $$7z - 15$$ is the simplest form it can take without knowing the value of z.
Beginning Algebra
Mastering the beginning stages of algebra is like learning to play chords on a guitar before writing a song. You learn the basics first; they鈥檙e the building blocks for solving more complex problems. Beginning algebra involves operations such as adding, subtracting, multiplying, and dividing numbers as well as understanding variables and expressions.

In practice, look at each term and operation in your expression. Ask yourself: 'Can I combine these terms? Should I distribute here?' Always look for an opportunity to simplify the expression, leading you step by step to a solution, like with our example, where we simplified $$5(z-3)+2z$$ to get $$7z - 15$$.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The perimeter of an equilateral triangle is at most 57 feet. What could be the length of a side? (Hint: All three sides of an equilateral triangle are equal.)

Solve each inequality and graph the solution on the number line. $$3 \leq 2 x-1 < 5$$

Solve each equation and round the result to the nearest tenth. $$\frac{-2.1(1.7 x+0.9)}{3.1}=-7.1(x-1.3)$$

Express each solution as an inequality. Geometry A rectangle's width is 8 feet less than 3 times its length, and its perimeter is between 8 and 16 feet. What might be its length?

The truss in the illustration is in the form of an isosceles triangle. Each of the two equal sides is 5 feet less than the third side. If the perimeter is 29 feet, find the length of each side.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.