Solving Two-Step Equations Involving Fractions

Mrs. Angel teaches how to solve equations involving fractions. The lesson covers the basic principles of moving multiplication into the numerator and using properties of equality to simplify equations. Two examples are provided: solving two-thirds of x equals eight and ten equals negative five-thirds times x. Students are encouraged to try solving negative four-fifths x equals negative ten on their own, with guidance on checking solutions and simplifying fractions.

What operations are primarily focused on in this lesson?

• Addition and Subtraction

• Multiplication and Division

• Exponentiation and Roots

• Logarithms and Trigonometry

In the equation 2/3x = 8, what is the first step to solve it?

• Divide by 8

• Subtract 2 from both sides

• Move the multiplication into the numerator

• Add 3 to both sides

After moving the multiplication into the numerator for 2/3x = 8, what is the new equation?

• 2x/3 = 8

• 2/3x = 8

• 2x = 24

• x/3 = 8

What is the final solution for the equation 2/3x = 8?

• x = 24

• x = 4

• x = 8

• x = 12

In the equation 10 = -5/3x, what happens to the negative sign when moving the multiplication into the numerator?

• It cancels out

• It moves with the x into the numerator

• It is ignored

• It stays with the denominator

What is the new equation after moving the multiplication into the numerator for 10 = -5/3x?

• 10 = -5x/3

• 10 = -5/3x

• 10 = -5x

• 10 = 5x/3

What is the solution for the equation 10 = -5/3x?

• x = 10

• x = -10

• x = 6

• x = -6

In the practice problem -4/5x = -10, what is the first step?

• Subtract 4 from both sides

• Move the multiplication into the numerator

• Divide by -10

• Add 5 to both sides

What is the simplified fraction solution for -4/5x = -10?

• 25/2

• 12/5

• 10/4

• 50/4

How can you check the solution for -4/5x = -10?

• By dividing both sides by -4

• By multiplying both sides by 5

• By adding the solution to both sides

• By substituting the solution back into the original equation