/*! 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 62 Solve $$-14 y=-168$$... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 62

Solve $$-14 y=-168$$

Short Answer

Expert verified
The solution to the equation is \(y = 12\)

Step by step solution

01

Identify the Equation

The equation given is: \(-14y = -168\). This is a linear equation in one variable.
02

Isolate y

To solve for y, we need to isolate y. We can do that by dividing both sides of the equation by -14. Remember, in mathematics, performing the same operation on both sides of an equation doesn't affect its equality. Hence, our new equation becomes: \(y = \frac{-168}{-14}\)
03

Simplify the Equation

Simplifying the equation gives us: \(y = 12\)

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Key Concepts

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

Solving Equations
Breaking down a problem into steps can make it easier to solve equations. In the world of mathematics, an equation is a statement that asserts the equality of two expressions. To solve it means to find the value of the unknown that makes the equation true. It requires isolating the variable you are solving for on one side of the equation.
Understanding the balance concept is crucial. Just like a balanced scale, both sides of the equation need to remain equal as you manipulate it. This balance can be achieved through:
  • Addition or subtraction
  • Multiplication or division
  • Combination of these operations
Every step in solving the equation must maintain this balance until you find the solution for the unknown variable.
One Variable Equations
One variable equations, like \(-14y = -168\), involve only one unknown quantity, which simplifies things a bit. The goal here is to find the value of the variable that ensures both sides of the equation are equal.
Starting with the equation \(-14y = -168\), notice that the variable \(y\) is multiplied by \(-14\). Thus, our aim is to 'unwind' this process, getting \(y\) to stand alone.
Upon isolating the variable, what's left is a straightforward equation where \(y\) equals a specific number. This makes learning one variable equations a fantastic stepping stone before tackling more complex equations with multiple variables.
Division in Algebra
Division is a common operation used to isolate the variable in algebra. In the example -14y = -168, we need to use division to solve for \(y\). To remove the \(-14\) attached to \(y\), divide both sides by \(-14\).
This step results in \(y = \frac{-168}{-14}\), simplifying to \(y = 12\). A key point to remember is that when both sides are negative, dividing them results in a positive answer.
To ensure success with division in algebra:
  • Always perform the same operation on both sides.
  • Double check for signs (positive/negative) as it affects the final answer.
  • Recheck your division to confirm the solution satisfies the original equation.
Develop comfort with division in algebra to build a strong foundation for solving various types of equations.

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Most popular questions from this chapter

In Exercises \(45-56,\) solve each system by the method of your choice. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. Explain why you selected one method over the other two. $$\left\\{\begin{array}{l} 2(x+y)=4 x+1 \\ 3(x-y)=x+y-3 \end{array}\right.$$

Involve dual investments. Your grandmother needs your help. She has 50,000 dollar to invest. Part of this money is to be invested in noninsured bonds paying \(15 \%\) annual interest. The rest of this money is to be invested in a government-insured certificate of deposit paying \(7 \%\) annual interest. She told you that she requires a total of 6000 dollar per year in extra income from these investments. How much money should be placed in each investment?

In Exercises \(57-60\), write a system of equations modeling the given conditions. Then solve the system by the addition method and find the two numbers. Three times a first number increased by twice a second number is \(11 .\) The difference between the first number and twice the second number is 9. Find the numbers.

One apartment is directly above a second apartment. The resident living downstairs calls his neighbor living above him and states, "If one of you is willing to come downstairs, we'll have the same number of people in both apartments." The upstairs resident responds, "We're all too tired to move. Why don't one of you come up here? Then we'll have twice as many people up here as you've got down there." How many people are in each apartment?

In Exercises \(61-68,\) solve each system or state that the system is inconsistent or dependent. $$\left\\{\begin{aligned} 1.25 x-1.5 y &=2 \\ 3.5 x-1.75 y &=10.5 \end{aligned}\right.$$
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