Solving Equations with Fractions and Decimals

The video tutorial explains how to solve equations involving fractions and decimals. It begins by discussing the importance of clearing fractions by multiplying through the equation. The elimination method is demonstrated for solving equations with aligned variables. The tutorial then shifts to solving equations with decimals using the substitution method, emphasizing the simplification of decimals by multiplying through by powers of ten. The video concludes with examples illustrating these methods, providing solutions to the equations.

What is the first step to simplify equations with fractions?

• Subtract fractions from both sides

• Divide by the smallest fraction

• Multiply to clear fractions

• Add fractions to both sides

When multiplying the first equation by 3, what is the result of 1/3 x 3?

• 3

• 1

• 1/3

• 9

What is the purpose of multiplying the second equation by 4?

• To increase the coefficients

• To clear away all fractions

• To make the equation more complex

• To reduce the coefficients

What method is preferred when one variable is isolated in an equation?

• Factoring

• Graphing

• Substitution

• Elimination

How do you eliminate decimals in an equation?

• Subtract decimals from both sides

• Divide by 10 or 100

• Multiply by 10 or 100

• Add decimals to both sides

What is the result of multiplying 0.3x by 10?

• 0.3x

• 3x

• 30x

• 0.03x

After clearing decimals, what is the equation to find x?

• 4x = 32

• 3x = 34

• 2x = 16

• 5x = 40

What is the value of x after solving the equation 4x = 32?

• 10

• 4

• 8

• 6

What is the value of y when x = 8 in the equation y = 0.2x + 0.4?

• 2.4

• 3

• 2

• 1.6

What is the final solution for the system of equations with decimals?

• (6, 4)

• (4, 6)

• (2, 8)

• (8, 2)