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Chapter 2: Problem 142

Translate to an equation and then solve. 187 is the product of -17 and \(m\).

Short Answer

Expert verified
m = -11

Step by step solution

01

Identify the relationship

The problem states that 187 is the product of -17 and a variable, which we can name as 'm'. This means that when -17 is multiplied by 'm', the result is 187.
02

Write the equation

Using the relationship identified, write the equation: \[-17m = 187\].
03

Solve for m

To find the value of 'm', divide both sides of the equation by -17: \[ m = \frac{187}{-17} \].
04

Simplify the solution

Carry out the division to simplify the solution: \[ m = -11 \].

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Key Concepts

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

algebra
Algebra is like a toolkit for solving mathematical problems that involve unknown numbers, often represented by variables such as 'm' in our exercise. It consists of rules and techniques for manipulating these variables and equations. In this particular problem, we use algebra to translate a word problem into a mathematical equation and then solve it. This equation helps us find the value of the unknown variable that satisfies the given condition.
linear equations
Linear equations involve expressions where each term is either a constant or the product of a constant and a single variable. The equation we solved, \(-17m = 187\), is an example of a linear equation. Such equations can be graphically represented by a straight line on a coordinate plane. Understanding linear equations is crucial because they form the basis for more complex algebraic concepts. They often pop up in real-life scenarios, such as calculating distances, budgeting, and predicting trends.
variable isolation
Variable isolation means rearranging an equation so that the unknown variable is on one side of the equation, and everything else is on the other side. In our example, \(-17m = 187\), isolating the variable 'm' requires us to move everything else (numbers, coefficients) away from 'm'. This is done to make 'm' the subject of the equation. Isolating 'm' in our problem involves dividing both sides of the equation by -17, which leaves us with \m = -11\. This process is fundamental for solving equations and helps simplify complex problems.
multiplication and division in equations
Multiplication and division are key operations when solving linear equations. These operations help us manipulate and simplify equations to isolate variables. In the given problem, \(-17m = 187\), we use division to isolate 'm'. Dividing both sides by -17 simplifies the equation, leading to \m = -11\. When performing these operations, remember to do the same thing to both sides of the equation to maintain the balance. Dividing a positive number by a negative number results in a negative quotient, as observed in our solution.

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Most popular questions from this chapter

Translate to an equation and then solve. The quotient of \(h\) and 26 is \(-52 .\)

Solve the following equations with variables and constants on both sides. $$13 z+6.45=8 z+23.75$$

Graph each inequality on the number line and write in interval notation. (a) \(\quad x \geq-4\) (b) \(\quad x<2.5\) (c) \(x>-\frac{3}{2}\)

Solve each equation with fraction coefficients. $$\frac{1}{2}(x+4)=\frac{3}{4}$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$6 y<48$$
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