Understanding Absolute Value and Fraction Equations

What is the first step in solving an absolute value equation?

• Square both sides of the equation

• Multiply both sides by a constant

• Isolate the absolute value expression

• Add a constant to both sides

When solving an absolute value equation, why do we create two separate equations?

• To check for extraneous solutions

• To account for both positive and negative solutions

• To eliminate fractions

• To simplify the equation

In the example where the absolute value of 2x + 8 equals 20, what are the solutions for x?

• x = 10 and x = -10

• x = 20 and x = -20

• x = 6 and x = -14

• x = 14 and x = -6

What happens if the isolated absolute value equals a negative number?

• The solution is negative

• There is no solution

• The solution is zero

• The solution is positive

What is the first step in solving a fraction equation?

• Subtract fractions on both sides

• Multiply by the reciprocal

• Add fractions on both sides

• Find a common denominator

Why do we multiply the entire equation by the common denominator when solving fraction equations?

• To eliminate fractions

• To simplify the equation

• To find the least common multiple

• To check for extraneous solutions

In the example with a common denominator of 12, what is the result after eliminating fractions?

• 3x + 4 = 10

• 4x + 3 = 10

• 6x + 1 = 10

• 5x + 2 = 10

What is the solution for x in the equation 3(x - 5) = 6 after eliminating fractions?

• x = 1

• x = 3

• x = 5

• x = 7

In the example with a common denominator of 8, what is the final solution for x?

• x = 3/2

• x = 5/4

• x = 7/8

• x = 9/16

What is the purpose of distributing after eliminating fractions in some fraction equations?

• To simplify the equation further

• To find the common denominator

• To check for extraneous solutions

• To isolate the variable