/*! 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 15 Solve $$3(6 x-10)=60$$ A. 18... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 15

Solve $$3(6 x-10)=60$$ A. 18 B. 5 C. 10 D. \(-18\)

Short Answer

Expert verified
The solution is B. 5.

Step by step solution

01

Distribute the 3

We start by distributing the 3 into the parentheses. This means we multiply both terms inside the parentheses by 3.\[3(6x - 10) = 3 \cdot 6x - 3 \cdot 10 = 18x - 30\]\So the equation becomes:\[18x - 30 = 60\]
02

Move constant to the other side

Next, we want to isolate the term with the variable by adding 30 to both sides of the equation.\[18x - 30 + 30 = 60 + 30\]\This simplifies to:\[18x = 90\]
03

Solve for x

Now, to solve for \(x\), we need to get \(x\) by itself by dividing both sides by 18.\[\frac{18x}{18} = \frac{90}{18}\]\This simplifies to:\[x = 5\]

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
When solving linear equations, the distributive property plays a crucial role. This property allows us to multiply a single term by the terms inside a set of parentheses. For example, in our exercise, we begin by distributing the 3 across the terms within the parentheses:
  • Multiply 3 by 6x, resulting in 18x
  • Multiply 3 by -10, giving -30
This step is vital because it eliminates the parentheses, simplifying the equation to a clear algebraic expression: \[ 18x - 30 = 60 \].
The distributive property is often a first step in solving equations because it helps remove grouping symbols, laying the groundwork for isolating the variable. This foundational step is often overlooked, but it streamlines the equation-solving process effectively.
Isolating the Variable
Once we've applied the distributive property, the next goal is to get the variable by itself on one side of the equation. This step is known as isolating the variable.
  • First, move constants from the side containing the variable to the other side of the equation. In our example, add 30 to both sides to remove the -30 next to 18x.
  • The equation becomes \(18x = 90\) after moving the constant.
By moving the constant term, we prepare the equation for the final step of isolation. It's crucial to perform the same operation on both sides of the equation to maintain balance. Think of this process as creating a singular, undisturbed spot for the variable to "sit" by itself.
Linear Equation Solutions
Finding a solution to a linear equation means determining the value of the variable that makes the entire equation true. Once the variable is isolated, solving it often involves simple arithmetic.
  • In our exercise, we had \(18x = 90\).
  • Divide both sides by 18 to solve for \(x\).
This gives:\[ x = \frac{90}{18} = 5 \].
Finding solutions in this way reveals the point where the equation holds true. This point, or solution, is where the expression equals its constant counterpart in real numbers. Successfully solving linear equations requires understanding steps like distribution and isolation, ensuring you can tackle more complex problems in algebra.

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 \(9 x=-108\). A. 15 B. \(-972\) C. \(-12\) D. \(-99\)

Solve \(x+51=43\). A. 94 B. \(-8\) C. \(-94\) D. 8

Find the wing loading (L) in pounds per square foot of an airplane when the gross weight (W) is \(6,300\) pounds and the wing area (A) is 450 square feet. Use $$L=\frac{W}{A}$$ A. 14 pounds per square foot B. 16 pounds per square foot C. 5 pounds per square foot D. 12 pounds per square foot

Combine like terms: \(2 y-4 x+8+6 y+x-7\) A. \(-3 x+8 y+1\) \(-5 x+4 y+15\) C. \(3 x+8 y-15\) D. \(3 x+8 y+15\)

\(45 \%\) of what number is \(405 ?\) Solve using an equation. A. 182.25 B. 900 C. 182.75 D. 9
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.