/*! 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 87 Solve. $$ 235=5 \cdot z $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 87

Solve. $$ 235=5 \cdot z $$

Short Answer

Expert verified
z = 47

Step by step solution

01

Identify the equation

The given equation is \[ 235 = 5 \cdot z \] where 235 is equal to 5 times a variable z.
02

Isolate the variable

To isolate z, divide both sides of the equation by 5. This gives: \[ z = \frac{235}{5} \]
03

Perform the division

Compute the division on the right side: \[ z = 47 \]
04

Verify the solution

Confirm by substituting z back into the original equation: \[ 5 \cdot 47 = 235 \] which is true.

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.

algebra
In algebra, we often work with equations that contain variables鈥攕ymbols that represent unknown values. These equations can involve various operations like addition, subtraction, multiplication, and division. The main goal is to find the value of the variable that makes the equation true. Understanding algebra is fundamental because it forms the basis for more advanced topics in mathematics.
When faced with an algebraic equation such as \[ 235 = 5 \cdot z \], we want to solve for the variable, in this case, 'z'. This process typically involves several steps: identifying the equation, isolating the variable, and performing necessary arithmetic operations to find the solution.
variable isolation
Isolating the variable is a crucial step in solving algebraic equations. This means manipulating the equation so that the variable in question stands alone on one side of the equality sign.
In the equation \[ 235 = 5 \cdot z \], 'z' is multiplied by 5. To isolate 'z', we need to undo the multiplication by dividing both sides of the equation by 5. This gives us: \[ z = \frac{235}{5} \]
By isolating the variable, we make it easier to see the solution directly. Always remember, whatever operation you do to one side of the equation, you must do to the other side to maintain equality.
division in equations
Division is one of the four basic arithmetic operations and is crucial when solving equations, particularly for isolating variables. In our example \[ 235 = 5 \cdot z \], we need to divide both sides by 5 to solve for 'z'. So, we compute: \[ z = \frac{235}{5} \]
This calculation simplifies to: \[ z = 47 \]
After performing the division, you should always check your solution. Plug 'z' back into the original equation to confirm: \[ 5 \cdot 47 = 235 \]
Since the left-hand side equals the right-hand side, the solution is verified and correct.

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

Solve. $$ 50=5 \cdot t $$

Find decimal notation for \(\frac{1}{9}, \frac{1}{99},\) and \(\frac{1}{999} .\) Observe the pattern and guess the decimal notation for \(\frac{1}{9999}\).

Rita's gross pay (before deductions) is \$495.72. Her deductions are \(\$ 59.60\) for federal income tax, \(\$ 29.00\) for FICA, and \(\$ 29.00\) for medical insurance. What is her take-home pay?

Claire bought a copy of the book Make Way for Ducklings for her daughter for \(\$ 16.95\) plus \(\$ 0.85\) sales tax. She paid for it with a \(\$ 20\) bill. How much change did she receive?

The water in a filled tank weighs \(748.45 \mathrm{lb}\). One cubic foot of water weighs \(62.5 \mathrm{lb}\). How many cubic feet of water does the tank hold?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Decision 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.