Solve each equation and check the result. If an equation has no solution, so indicate. (1)/(8)+(

step 1 To solve this equation, we are going to multiply both sides by the LCD. So the LCD in this case

Solve each equation and check the result. If an equation has...

Key Concepts

Rational Equations

Rational equations are equations involving fractions whose numerators and/or denominators contain algebraic expressions. Solving these equations often requires finding a common denominator or clearing fractions to avoid dealing directly with the fractional form, while also being mindful of any restrictions on the variable (such as values that would make a denominator zero).

Common Denominator

Finding a common denominator is a technique used to combine or compare rational expressions. By expressing fractions with a shared denominator, one can easily perform addition or subtraction, simplify the equation, and eliminate the fractions to work with a simpler algebraic equation.

Linear Equations

Linear equations are equations of the first degree, meaning that the variable is raised to the power of one. Solving linear equations involves isolating the variable using algebraic operations such as addition, subtraction, multiplication, and division. They form the foundation of more complex algebraic techniques.

Checking Solutions

After solving an equation, it is essential to substitute the found solution back into the original equation to verify that it satisfies the equation. This process, known as checking solutions, helps to confirm that no errors were made during the manipulation or that extraneous solutions were not introduced, particularly in equations involving rational expressions.

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