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Chapter 2: Problem 44

Solve each equation, and check the solution. $$ 0.8 x=-2.96 $$

Short Answer

Expert verified
The solution is \( x = -3.7 \). Verified by substitution.

Step by step solution

01

Isolate the variable

To isolate the variable \( x \) in the equation \( 0.8x = -2.96 \), divide both sides of the equation by 0.8.
02

Perform the division

Divide \( -2.96 \) by 0.8. \[ x = \frac{-2.96}{0.8} \] Simplifying, \[ x = -3.7 \]
03

Check the solution

To verify the solution, substitute \( x = -3.7 \) back into the original equation. \[ 0.8(-3.7) = -2.96 \] Since both sides are equal, \( x = -3.7 \) is the correct solution.

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Key Concepts

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

isolation of variables
To solve a linear equation like \(0.8x = -2.96\), the first step is to isolate the variable. This means getting the variable \(x\) alone on one side of the equation. Removing any numbers or coefficients directly attached to \(x\).
In this case, \(0.8\) is multiplied by \(x\). To isolate \(x\), we need to reverse that multiplication. The reverse operation of multiplication is division. This leads to our next step in achieving isolation: division in algebra.
division in algebra
In algebra, division is often used to solve for variables. By dividing both sides of an equation by the same number, we can maintain equilibrium in the equation. It鈥檚 like balancing scales; whatever you do to one side, do to the other.
Given \(0.8x = -2.96\), we divide both sides by \(0.8\):
\[ x = \frac{-2.96}{0.8} \]
When we simplify, we find \(x\):
\[ x = -3.7 \]

This means \(x\) has been isolated, and its value solved through the division process. It is crucial to perform this operation carefully to ensure the solution is correct.
solution verification
After isolating the variable and solving for \(x\), it's important to verify that the solution is correct. Verification ensures that no mistakes were made during the calculation.
  • Substitute \(x = -3.7\) back into the original equation:
    \[ 0.8(-3.7) = -2.96 \]
  • Calculate the left side:
    \[ 0.8 \times -3.7 = -2.96 \]
  • Both sides match perfectly, confirming the solution is correct.
Always check your work to confirm accuracy. This step reassures you that the answer holds true and that you followed the correct process.

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Most popular questions from this chapter

The world's largest taco contained approximately \(1 \mathrm{~kg}\) of onion for every \(6.6 \mathrm{~kg}\) of grilled steak. The total weight of these two ingredients was \(617.6 \mathrm{~kg}\). To the nearest tenth of a kilogram, how many kilograms of each ingredient were used to make the taco? (Data from Guinness World Records.

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