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Chapter 5: Problem 24

Solve the equations. $$94.08=-8.4 q$$

Short Answer

Expert verified
q = -11.2

Step by step solution

01

Understand the Equation

The given equation is \[ 94.08 = -8.4q \]. We need to solve for the variable \( q \).
02

Isolate the Variable

To isolate \( q \), divide both sides of the equation by -8.4: \[ q = \frac{94.08}{-8.4} \]
03

Perform the Division

Calculate the value of the right-hand side: \[ q = -11.2 \]

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Key Concepts

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

Isolating the Variable
In equations, isolating the variable is a crucial step. It simply means getting the variable you're solving for to stand alone on one side of the equation.
Here, our equation is: \[ 94.08 = -8.4q \] The variable we need to isolate is \( q \).
Imagine you're solving a mystery and the first thing you need to do is gather all clues in one spot. Similarly, we gather everything involving \( q \) to one side of our equation.
In our case, we can see that \( -8.4q \) is multiplied by \(-8.4\). To isolate \( q \), we need to undo this multiplication by performing the opposite operation, which is division.
Division in Equations
Division is a common method to isolate a variable in linear equations.
When you have an equation like \( -8.4q \), you can divide both sides by \(-8.4\). This balances out the equation.
Tip: Always remember to do the same operation on both sides to keep the equation balanced.
For instance, in our exercise: \[ 94.08 = -8.4q \] Divide both sides by \(-8.4\): \[ q = \frac{94.08}{-8.4} \] Now we have succeeded in getting \( q \) alone!
This is how division works in equations to isolate the variable.
Negative Numbers
Working with negative numbers in equations can seem tricky, but it's easy if you break it down.
Negative signs simply indicate the opposite direction on the number line.
If you divide or multiply both sides of an equation by a negative number, the result will change signs.
In our exercise, dividing by \(-8.4\) changes the sign of the result: \[ q = \frac{94.08}{-8.4} \] This gives us: \[ q = -11.2 \] Understanding this helps to avoid mistakes.
Never forget:
  • Positive 梅 Negative = Negative
  • Negative 梅 Negative = Positive
  • Negative 脳 Negative = Positive
  • Positive 脳 Negative = Negative
With this in mind, handling negative numbers can become much easier and predictable.

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Most popular questions from this chapter

The average speed, in miles per hour (mph), of the Daytona 500 for selected years is given in the table. Rank the speeds from slowest to fastest. (Source: NASCAR) $$\begin{array}{|l|l|l|} \hline \text { Year } & \text { Driver } & \text { Speed (mph) } \\ \hline 1989 & \text { Darrell Waltrip } & 148.466 \\ \hline 1991 & \text { Ernie Irvan } & 148.148 \\ \hline 1997 & \text { Jeff Gordon } & 148.295 \\ \hline 2007 & \text { Kevin Harvick } & 149.333 \\ \hline \end{array}$$

Certain DVD titles are on sale for 2 for \(\$ 32\). If they regularly sell for \(\$ 19.99,\) how much can a person save by buying 4 DVDs?

The table shows the thickness of four U.S. coins. If you stacked three quarters and a dime in one pile and two nickels and two pennies in another pile, which pile would be higher? $$\begin{array}{l|l} \text { Coin } & \text { Thickness } \\ \hline \text { Quarter } & 1.75 \mathrm{mm} \\ \hline \text { Dime } & 1.35 \mathrm{mm} \\ \hline \text { Nickel } & 1.95 \mathrm{mm} \\ \hline \text { Penny } & 1.55 \mathrm{mm} \\ \hline \end{array}$$

Perform the indicated operations. Round the answer to the nearest hundredth when necessary. $$\left(\frac{1}{12}\right)(6.24) \div(-2.1)$$

Divide. Round the answer to the indicated place value. Use the rounded quotient to check. $$27.88 \div 2.46 \text { thousandths }$$
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