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Chapter 5: Problem 15

Solve the equations. $$-141.2=-91.3+p$$

Short Answer

Expert verified
p = -49.9

Step by step solution

01

Isolate the variable

To solve for the variable p, add 91.3 to both sides of the equation to get:-141.2 + 91.3 = -91.3 + p + 91.3
02

Simplify both sides

Simplify the equation by performing the addition on both sides: -141.2 + 91.3 = p. This results in: -49.9 = p
03

Rewrite the solution

Finally, rewrite the simplified equation as p = -49.9.

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Key Concepts

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

Isolating the Variable
In linear equations, isolating the variable is the first key step to finding its value. It means getting the variable by itself on one side of the equation. This allows us to solve for it directly. For instance, in the equation ewlineewline $$-141.2 = -91.3 + p$$, we want to isolate p. To achieve this, we need to eliminate the term on the same side as p. We do this by performing the same operation on both sides. Here, we add 91.3 to both sides: ewlineewline ewlineewline-141.2 + 91.3 = -91.3 + p + 91.3. ewlineewline Notice that now, all terms except p are on the left side. Our next step is to simplify this equation.
Simplifying Equations
Simplifying an equation involves performing arithmetic operations to combine like terms and make the equation easier to understand. After isolating the variable, we had: ewlineewlineewlineewline-141.2 + 91.3 = p. ewlineewline ewlineewlineNow we simplify by carrying out the addition on the left side. Subtract 91.3 from 141.2 to get: ewlineewline -49.9 = p. Simplifying helps us see the actual value of the variable more clearly. Always double-check your arithmetic to avoid mistakes!
Addition Property of Equality
The addition property of equality is a fundamental principle used frequently in solving equations. It tells us that if we add the same amount to both sides of an equation, the equality holds true. For example, in ewlineewlineewlineewline-141.2 = -91.3 + p, we added 91.3 to both sides: ewlineewline-141.2 + 91.3 = -91.3 + p + 91.3. ewlineewline This allowed us to eliminate the -91.3 term on the right. Since we're doing the same operation to both sides, the equation remains balanced and valid. By applying the addition property of equality, we ensure the left and right sides stay equal throughout the solving process.

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