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Chapter 5: Problem 25

Solve the equations. $$-6.2 y=-117.8$$

Short Answer

Expert verified
The solution is \( y = 19 \).

Step by step solution

01

Isolate the variable

To solve for the variable \( y \), divide both sides of the equation by the coefficient of \( y \), which is \(-6.2\). This gives: \[ y = \frac{-117.8}{-6.2} \]
02

Simplify the expression

Now, simplify the right-hand side of the equation. Perform the division: \[ y = \frac{-117.8}{-6.2} = 19 \]

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Key Concepts

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

Isolate the Variable
When solving an equation, the goal is to isolate the variable on one side. This means you need to get the variable by itself. In our example, the variable is \( y \). The equation given is \({-6.2y = -117.8}\). To isolate \( y \), we need to remove the \(-6.2\) that is being multiplied by \( y \).

To do this, we use division because it is the opposite operation of multiplication. We divide both sides of the equation by \( -6.2 \).

Hence, \( y \) is isolated: \[ y = \frac{-117.8}{-6.2} \]. This step is crucial as it simplifies the equation to find the value of the variable.
Coefficient
A coefficient is a number multiplying the variable in an equation. In our example equation \( -6.2y = -117.8 \), the coefficient of \( y \) is \(-6.2\).

The coefficient tells you how many times to multiply the variable by. To isolate the variable, we need to undo this multiplication. Hence, you divide both sides of the equation by the coefficient.

By understanding what a coefficient is, it helps you comprehend why we perform certain operations to isolate the variable.
Simplify Division
After isolating the variable, the next step is to simplify the division. Once we have \[ y = \frac{-117.8}{-6.2} \], we must perform the actual division.

To simplify, divide \( -117.8 \) by \( -6.2 \): \[ y = 19 \] . Use a calculator if needed, ensuring accuracy.

Proper simplification ensures you get the correct answer.
Negative Numbers
Dealing with negative numbers is essential in solving equations. In our example, both the coefficient and the constant are negative: \(-6.2\) and \(-117.8 \).

When dividing two negative numbers, the result is positive because a negative divided by a negative equals a positive. Hence, \[ \frac{-117.8}{-6.2} = 19 \].

Remembering this rule helps avoid mistakes and ensures correct solutions when dealing with negative numbers.

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Most popular questions from this chapter

The Athletic Department at Broward College bought 20 pizzas for \(\$ 10.95\) each, 10 Greek salads for \(\$ 3.95\) each, and 60 soft drinks for \(\$ 0.60\) each. What was the total bill including a sales tax of \(\$ 17.67 ?\)

Perform the indicated operations. Round the answer to the nearest hundredth when necessary. $$6.5 \div\left(-\frac{3}{5}\right)$$

Solve the application. Check to see if your answers are reasonable. Ty Cobb was at bat 11,434 times and had 4189 hits, giving him the all-time best batting average. Find his average. Round to the thousandths place.

One megawatt (MW) of wind power produces enough electricity to supply approximately 275 homes. For a recent year, the state of Texas produced \(3352 \mathrm{MW}\) of wind power. (Source: American Wind Energy Association) a. About how many homes can be supplied with electricity using wind power produced in Texas? b. The given table outlines new proposed wind power projects in Texas. If these projects are completed, approximately how many additional homes could be supplied with electricity? $$\begin{array}{l|c} \text { Project } & \text { MW } \\ \hline \text { JD Wind IV } & 79.8 \\ \hline \text { Buffalo Gap, Phase II } & 232.5 \\ \hline \text { Lone Star I (3Q) } & 128 \\ \hline \text { Sand Bluff } & 90 \\ \hline \text { Roscoe } & 209 \\ \hline \text { Barton Chapel } & 120 \\ \hline \text { Stanton Wind Energy Center } & 120 \\ \hline \text { Whirlwind Energy Center } & 59.8 \\ \hline \text { Swcetwater V } & 80.5 \\ \hline \text { Champion } & 126.5 \\ \hline \end{array}$$

For Exercises \(83-88\) simplify by $$(78.2-60.2) \div \frac{9}{13}$$
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