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Chapter 2: Problem 45

Solve each equation, and check the solution. $$ -9.1=-2.6 x $$

Short Answer

Expert verified
x = 3.5

Step by step solution

01

- Identify the equation

The given equation is: -9.1 = -2.6 x
02

- Isolate the variable

To isolate the variable x, divide both sides of the equation by -2.6: \[ \frac{-9.1}{-2.6} = x \]
03

- Simplify the division

Now, calculate the division on the left side: \[ x = \frac{-9.1}{-2.6} = 3.5 \]
04

- Check the solution

To verify the solution, substitute x back into the original equation and check if both sides are equal: \[-2.6 (3.5) = -9.1 \] Since -9.1 = -9.1, the solution is correct.

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Key Concepts

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

Isolate Variable
When solving linear equations, one of the first steps is to isolate the variable. This means getting the unknown variable (in this case, x) on one side of the equation, and everything else on the other side.
For our example, the equation is -9.1 = -2.6x.
To isolate x, we need to remove the coefficient (the number attached to x, here -2.6). We will do this using division, which leads us to our next concept.
Division in Equations
Division is a key tool in solving equations where the variable has a coefficient. Here, we have -9.1 = -2.6x.
To isolate x, divide both sides of the equation by -2.6:
\( \frac{-9.1}{-2.6} = x \)
Remember to treat both sides of the equation equally to maintain the balance. When you do the division:
\( x = \frac{-9.1}{-2.6} = 3.5 \)
Now x is isolated and equals 3.5. Let's move on to checking our solution.
Checking Solutions
After solving an equation, it鈥檚 important to check if the solution is correct. This verifies our work.
To check, substitute the solution back into the original equation and see if the left-hand side equals the right-hand side.
For our example, we substitute x = 3.5 back into -9.1 = -2.6x:
\(-9.1 = -2.6 \times 3.5\)
Simplify the multiplication: \-9.1 = -9.1\
Since both sides of the equation match, our solution x = 3.5 is correct.
Following these steps ensures accuracy in solving linear equations.

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