Solving Linear Equations with Fractions

This video tutorial demonstrates how to solve a linear equation in one variable with fractions. It covers two methods: clearing fractions using the least common denominator and solving directly with fractions. The tutorial explains each step, including isolating the variable and verifying the solution through substitution. The video emphasizes creating equivalent equations by performing the same operations on both sides.

What is the primary goal when solving linear equations with fractions?

• To simplify the equation to a single number

• To eliminate all variables

• To create equivalent equations

• To find the least common denominator

What is the least common denominator used to clear fractions in the given example?

• 20

• 15

• 30

• 45

After clearing fractions, what is the next step in solving the equation?

• Add or subtract to isolate the variable term

• Multiply both sides by zero

• Divide both sides by the variable

• Add fractions back into the equation

What operation is performed to isolate the variable x in the equation 24x = 25?

• Subtract 24 from both sides

• Add 24 to both sides

• Divide both sides by 24

• Multiply both sides by 24

When solving without clearing fractions, what is the first step to isolate the variable term?

• Divide by the least common denominator

• Multiply by the reciprocal of the fraction

• Subtract two-thirds from both sides

• Add two-thirds to both sides

What is the reciprocal of four-fifths used in the alternative solving method?

• Five-thirds

• Four-fifths

• Five-fourths

• One-fourth

What is the final solution for x in the equation using either method?

• 24/25

• 25/24

• 3/2

• 5/6

How do you verify the solution of a linear equation?

• By multiplying the solution by the original equation

• By checking if both sides of the equation are equal after substitution

• By adding the solution to both sides of the equation

• By dividing the solution by the least common denominator

What is the result of substituting x = 25/24 back into the original equation?

• The left side equals 1.5

• The right side equals 2

• Both sides equal 3/2

• Both sides equal 5/6

What tool is suggested to quickly verify the solution of the equation?

• A calculator

• A ruler

• A protractor

• A graphing paper