/*! 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 69 Solve each equation, and check y... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 69

Solve each equation, and check your solution. $$ 0.006(x+2)=0.007 x+0.009 $$

Short Answer

Expert verified
x = 3

Step by step solution

01

Distribute the 0.006

First, distribute the 0.006 across the terms inside the parentheses: \[ 0.006(x + 2) = 0.006x + 0.012 \]So the equation becomes:\[ 0.006x + 0.012 = 0.007x + 0.009 \]
02

Isolate the variable terms on one side

Subtract 0.006x from both sides to start isolating x:\[ 0.012 = 0.001x + 0.009 \]
03

Isolate x

Subtract 0.009 from both sides:\[ 0.012 - 0.009 = 0.001x \]This simplifies to:\[ 0.003 = 0.001x \]
04

Solve for x

Divide both sides by 0.001:\[ x = \frac{0.003}{0.001} = 3 \]
05

Check the solution

Substitute x = 3 back into the original equation to check:\[ 0.006(3 + 2) = 0.007(3) + 0.009 \]This gives:\[ 0.006(5) = 0.021 + 0.009 \]\[ 0.03 = 0.03 \]Since both sides are equal, x = 3 is correct.

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.

Distribution in Algebra
When solving linear equations, one useful technique is distribution.
Distribution means to multiply each term inside parentheses by a factor outside of them.
For instance, in the given problem, we have the term \(0.006(x+2)\).
To eliminate the parentheses, we multiply 0.006 by both \(x\) and 2:
\[ 0.006 \times x = 0.006x \]
\[0.006 \times 2 = 0.012 \].
This helps simplify the equation, making it easier to solve.
In general, always remember that:
\[ a(b + c) = ab + ac \]
This principle is used extensively in algebra to clear parentheses and simplify expressions.
Isolating the Variable
After distributing, the next key step is to isolate the variable.
The variable is the unknown value we are trying to solve for, often represented by \(x\).
To isolate the variable, we need to get it alone on one side of the equation.
Here鈥檚 a systematic way to do this:
  • First, move all variable terms to one side. In our problem, we subtract 0.006x from both sides to get: \[ 0.012 = 0.001x + 0.009 \]
  • Next, move the constant term to the other side. Subtract 0.009 from both sides:
    \[ 0.012 - 0.009 = 0.001x \]
  • Finally, divide by the coefficient of x to solve for it:
    \[ x = \frac{0.003}{0.001} = 3 \]

Remember, each step requires performing the same operation on both sides of the equation.
Checking Solutions
It鈥檚 good practice to check your solution to ensure it鈥檚 correct.
To do this, substitute the value you found back into the original equation.
For our example, substituting x = 3 gives:
\[ 0.006(3 + 2) = 0.007(3) + 0.009 \]
Simplify both sides:
\[ 0.006 \times 5 = 0.03 \]
\[ 0.021 + 0.009 = 0.03 \]
Since both sides of the equation are equal, the solution is confirmed.
This step is crucial as it validates your work and ensures no mistakes were made during the calculations.

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

In each of the following, (a) translate as an expression and (b) translate as an equation or inequality. Use x to represent the number. (a) 8 less than a number (b) 8 is less than a number.

Solve each formula for the specified variable. \(P=a+b+c\) (perimeter of a triangle) (a) for \(b\) (b) for \(c\)

Grant Wood painted his most famous work, American Gothic, in 1930 on composition board with perimeter 108.44 in. If the painting is 5.54 in. taller than it is wide, find the dimensions of the painting. (Source: The Gazette.)

Solve each equation. $$ x+0.20 x=66 $$

In each of the following, (a) translate as an expression and (b) translate as an equation or inequality. Use x to represent the number. (a) 15 more than a number (b) 15 is more than a number.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.