Solving Linear Equations Concepts

In this Eureka Math lesson, Mr. Schenkel guides eighth-grade students through solving linear equations using various properties of equality. The lesson covers the commutative and distributive properties, combining like terms, and using reciprocals for division. Students learn to strategically apply these properties to isolate variables and solve equations. The lesson includes multiple examples and emphasizes understanding the underlying principles to handle equations involving fractions.

What is the main goal when solving a linear equation?

• To convert the equation into a quadratic form

• To eliminate all variables from the equation

• To make both sides of the equation identical

• To find the value of the variable that makes the equation true

Which property allows you to add the same number to both sides of an equation?

• Commutative Property

• Multiplication Property of Equality

• Distributive Property

• Addition Property of Equality

When simplifying an expression, what is the first step?

• Add constants to both sides

• Multiply by the reciprocal

• Combine like terms

• Isolate the variable

What is the reciprocal of 2/3?

• 3/1

• 1/3

• 2/3

• 3/2

How do you handle division by a fraction when solving equations?

• Divide by the fraction directly

• Multiply by the reciprocal of the fraction

• Add the fraction to both sides

• Convert the fraction to a decimal

What is the result of subtracting 3x from both sides of the equation 6x + 4 = 3x - 1?

• 3x + 4 = -1

• x = 3

• 6x = 3x - 1

• 3x = -5

In the equation 5/5x - 9 = 3/5x, what is the first step to isolate x?

• Divide by 3

• Add 9 to both sides

• Subtract 3/5x from both sides

• Multiply by 5

What is the solution to the equation 29 - 3x = 5x + 5?

• x = -5

• x = -3

• x = 3

• x = 5

How do you simplify the expression 1/3x + 166 = x?

• Divide by 166

• Add 166 to both sides

• Subtract 1/3x from both sides

• Multiply by 3

What is the final solution for x in the equation 1/3x + 166 = x?

• x = 45/2

• x = 264

• x = 88

• x = 3