Solve each equation, and check your solution. (1)/(2) x+5=-(1)/(2) x

Name: Problem 49, Chapter 2: Beginning Algebra
Uploaded: 2020-06-18T18:24:31-08:00
Duration: 1 min 39 s
Channel: Matt Gibson
Description: Solve each equation, and check your solution. (1)/(2) x+5=-(1)/(2) x

step 1 Since I have variables on both sides for this equation, I need to use the opposite operation to

Solve each equation, and check your solution. (1)/(2)...

Key Concepts

Linear Equations

Linear equations are algebraic equations in which the highest power of the variable is one. They usually take the form ax + b = 0, and solving them involves finding the value of the variable that makes the equation true. This concept is fundamental in algebra and serves as the basis for understanding more complex equations and systems.

Solving Linear Equations

The process of solving linear equations involves techniques such as isolating the variable, combining like terms, and applying inverse operations (such as addition or subtraction, multiplication or division) to both sides of the equation. These methods ensure that the equality is maintained while simplifying the equation until the variable’s value can be explicitly determined.

Checking Solutions

Checking solutions is an important step in solving equations where the found value is substituted back into the original equation to verify that it satisfies the equality. This process helps to confirm the accuracy of the result and to catch any errors made during the manipulation of the equation.

Operations with Rational Numbers

Operations with rational numbers, including fractions, are often integrated into solving equations where coefficients are fractional. Mastery of addition, subtraction, multiplication, and division of rational numbers is essential in solving such equations accurately, ensuring that the manipulation of these terms is done correctly throughout the solution process.

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