/*! 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 86 Find \(c\) such that \(x=2\) is ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 86

Find \(c\) such that \(x=2\) is a solution of the linear equation \(5 x+2 c=12+4 x-2 c\)

Short Answer

Expert verified
The value of \(c\) for which \(x = 2\) is a solution for the given equation is \(2.5\).

Step by step solution

01

Simplify the equation

First simplify the equation and move all terms to one side if necessery to get the equation into a standard form. As the equation is \(5x + 2c = 12 + 4x - 2c\), simplifying it gives \(5x - 4x + 2c + 2c = 12\), which further simplifies to \(x + 4c = 12\).
02

Substitute given value of \(x\)

Now, substitute \(x = 2\) into the simplified equation. This gives \(2 + 4c = 12\).
03

Solve for \(c\)

Subtract 2 from both sides of this equation, yields \(4c = 12 - 2 = 10\), and finally divide by 4 to solve for \(c\), resulting in \(c = 10/4 = 2.5\).

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.

Understanding Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It's about finding the unknowns or figuring out how different variables interact. In the context of equations like the one in the exercise, we use algebra to express relationships and solve for unknown variables, such as \(c\) in this exercise.

Algebra typically involves variables (like \(x\) or \(c\)), constants, and arithmetic operations (addition, subtraction, multiplication, and division). Understanding how to manipulate and simplify these expressions is key to solving algebraic equations.

By substituting values and rearranging terms, we can focus on what the equation is asking us to solve. This allows us to find a solution by determining what values the variables must take to satisfy the equation.
Solving Linear Equations
Solving linear equations means finding the values of variables that make the equation true. Linear equations are the simplest form of equations in algebra, often involving variables raised to the power of one. The primary goal is to isolate the variable on one side of the equation to find its value.

To solve the equation from the exercise, follow key steps:
  • First, simplify the equation: collect like terms and get it into a standard format, such as \(ax + b = c\).
  • Substitute the known value鈥攊n this exercise \(x = 2\)鈥攊nto the equation.
  • Rearrange the equation to isolate the variable you are solving for, which is \(c\) in this case.
  • Perform operations such as addition, subtraction, multiplication, or division to solve for the unknown.
Linear equations typically have one solution, and finding this solution involves a series of logical steps that must be followed carefully.
Simplification of Equations
Simplification in algebra involves modifying an equation to make it easier to solve. This process usually involves combining like terms, conducting arithmetic operations, and eliminating unwanted terms from one side of the equation.

In the provided exercise, simplifying the equation helps us bring the problem to a more manageable form. For example, we started with \(5x + 2c = 12 + 4x - 2c\) and simplified it to \(x + 4c = 12\).

Key simplification steps include:
  • Combining like terms: Combine terms with the same variable, like \(x\) terms and constant terms.
  • Rearranging the equation: It's often helpful to move all variables to one side of the equation and constants to the other.
  • Maintaining equation balance: Whatever operation you perform on one side, perform on the other to keep the equation equal.
This simplification forms the basis for effectively solving the equation and reaching the correct solution.

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 the inequality and graph the solution on the real number line. Use a graphing utility to verify your solution graphically. $$x^{5}-3 x^{4} \leq 0$$

use the models below, which approximate the numbers of Bed Bath \(\&\) Beyond stores \(B\) and Williams-Sonoma stores \(W\) for the years 2000 through \(2013,\) where \(t\) is the year, with \(t=0\) corresponding to 2000. (Sources: Bed Bath \(\&\) Beyond, Inc.; Williams-Sonoma, Inc.) Bed Bath \& Beyond: $$B=86.5 t+342,0 \leq t \leq 13$$ Williams-Sonoma: $$W=-2.92 t^{2}+52.0 t+381,0 \leq t \leq 13$$. Solve the equation \(B(t)=W(t) .\) Explain what the solution of the equation represents.

Solving a Quadratic Equation Find all real solutions of the equation. $$x^{2}-22 x+121=0$$

Solving a Quadratic Equation Find all real solutions of the equation. $$x(x-20)+3(x-20)=0$$

Solve the inequality and graph the solution on the real number line. Use a graphing utility to verify your solution graphically. $$\frac{1}{x}-4<0$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.