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Chapter 5: Problem 293

In the following exercises, solve the equation. $$ a+6.2=-1.7 $$

Short Answer

Expert verified
a = -7.9

Step by step solution

01

- Isolate the variable

To isolate the variable, subtract 6.2 from both sides of the equation. This will give us: a + 6.2 - 6.2 = -1.7 - 6.2
02

- Simplify both sides

Simplify the equation by performing the subtraction on both sides. We get: a = -7.9

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Key Concepts

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

Isolating the Variable
The first step when solving a linear equation is to isolate the variable. This means we want to get the variable by itself on one side of the equation. In the given exercise, our equation is:

\( a + 6.2 = -1.7 \).
To isolate 'a', we need to undo the addition of 6.2. This is done by performing the opposite (or inverse) operation.

  • The opposite of addition is subtraction.
  • So, we subtract 6.2 from both sides of the equation.

By doing this, we keep the equation balanced. Here's what it looks like:

\[a + 6.2 - 6.2 = -1.7 - 6.2\]

On the left side, the +6.2 and -6.2 cancel each other out, leaving us with just 'a'. Now we've successfully isolated the variable!
Simplifying Equations
Once we've isolated the variable, we move on to simplifying both sides of the equation. Simplifying means performing the arithmetic operations to transform the equation into a simpler form. Let's take a look at our simplified equation after isolating the variable:

\[a = -1.7 - 6.2\]

Here, we have to perform the subtraction on the right-hand side of the equation. Simplification step by step can involve the following:
  • Breaking down complex arithmetic operations into simpler steps.
  • Performing operations like addition, subtraction, multiplication, and division methodically.
In our case, we need to perform the subtraction:

\[-1.7 - 6.2\]

By carrying out this subtraction, we get:
\[a = -7.9\]

Now our equation is fully simplified to
\[a = -7.9\]
Arithmetic Operations
Understanding arithmetic operations is key to solving linear equations effectively. The basic operations include:
  • Addition (+)
  • Subtraction (鈭�)
  • Multiplication (脳)
  • Division (梅)

In our exercise, the primary arithmetic operation we used was subtraction. Here鈥檚 a quick refresher:

When you see an equation like
\[a + 6.2 = -1.7\] we used subtraction to isolate the variable on one side.
We performed the operation
\[-1.7 - 6.2\]
To handle this:
  • Keep in mind the rules for adding and subtracting negative numbers.
  • In this case, subtracting a positive number (6.2) from a negative number (-1.7) makes the result more negative.
This kind of understanding helps you quickly and accurately solve linear equations. Practicing these arithmetic operations will sharpen your skills and make solving equations easier.

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Most popular questions from this chapter

In the following exercises, round each number to the nearest tenth. $$0.67$$

In the following exercises, locate each number on a number line. $$0.8$$

In the following exercises, order each of the following pairs of numbers, using < or >. $$0.86\underline\quad0.69$$

A popular fast food burger weighs 7.5 ounces and contains 540 calories, 29 grams of fat, 43 grams of carbohydrates, and 25 grams of protein. Find the unit rate of (a) calories per ounce (b) grams of fat per ounce (c)grams of carbohydrates per ounce (d) grams of protein per ounce. Round to two decimal places.

In the following exercises, order each of the following pairs of numbers, using < or >. $$0.7\underline\quad0.8$$
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