Solving Equations with Decimals

This video tutorial covers solving multi-step linear equations involving decimals. It begins with guidelines for solving such equations, including removing parentheses, combining like terms, and isolating variable and constant terms. Two examples are provided, demonstrating the process of solving equations step-by-step, including checking solutions for accuracy.

What is the first step in solving a multi-step equation involving decimals?

• Add or subtract terms

• Multiply or divide terms

• Check the solution

• Remove parentheses using the distributive property

In the first example, what is the result of combining the like terms 1.2X and -0.9X?

• 0.9X

• 2.1X

• 0.3X

• 1.1X

What operation is performed to isolate the variable term in the equation 0.3X - 5.12 = 1.6?

• Divide both sides by 0.3

• Multiply both sides by 0.3

• Add 5.12 to both sides

• Subtract 5.12 from both sides

How do you make the divisor a whole number when dividing 6.72 by 0.3?

• Add a zero to the divisor

• Move the decimal point to the left

• Move the decimal point to the right

• Subtract 0.3 from the divisor

What is the solution for X in the equation 0.3X = 6.72?

• X = 22.4

• X = 224

• X = 2.24

• X = 0.224

In the second example, what is the result of distributing -0.2 across the terms in the parentheses?

• 5X + 0.2X

• 5X - 0.84

• 5X - 0.2X

• 5X + 0.84

What is the combined result of the like terms 5X and -0.2X in the second example?

• 4.2X

• 5.8X

• 5.2X

• 4.8X

What is the final step to solve the equation 4.8X = 0.96?

• Divide both sides by 4.8

• Add 0.96 to both sides

• Subtract 0.96 from both sides

• Multiply both sides by 4.8

What is the solution for X in the equation 4.8X = 0.96?

• X = 2

• X = 0.2

• X = 20

• X = 0.02

How do you verify the solution for X in the second example?

• By multiplying the solution by 2

• By adding the solution to both sides

• By dividing the solution by 2

• By substituting X back into the original equation