Solving Basic Algebraic Equations

This lesson covers various mathematical concepts related to balance and equations. Students learn to select and write equations representing hangers, reason with equations to find unknown values, and match equations to diagrams. The lesson also includes practical applications such as calculating side lengths of rectangles given the area and determining savings as a percentage of a goal.

What is the main focus of Unit 6 Lesson 3?

• Understanding fractions

• Staying in balance

• Learning about geometry

• Exploring algebraic expressions

Which equation represents the hanger with three x's balancing with six ones?

• x + x = 1 + 1 + 1 + 1

• 3x = 5

• x + x + x = 1 + 1 + 1 + 1 + 1 + 1

• x = 6

What is the value of x if 3x equals 6?

• 1

• 6

• 3

• 2

What is the correct reasoning to find x in the equation 3x = 6?

• Add 3 to both sides

• Multiply both sides by 3

• Divide both sides by 3

• Subtract 3 from both sides

How can you represent a hanger with two x's and three ones?

• x + 3

• x = 3

• 2x + 3

• 2x = 3

What is the equation for a hanger with three y's balancing with 5.1?

• 3y = 5.1

• y + y + y = 5.1

• 3y = 6

• y = 5.1

What is the equation for a hanger with z plus one-third balancing with one-half?

• z + 1/3 = 1/2

• z = 1/3

• z = 1/2

• z + 1/2 = 1/3

What is the equation for a hanger with w plus 1.3 balancing with 2.7?

• w = 1.3

• w + 2.7 = 1.3

• w = 2.7

• w + 1.3 = 2.7

What is the equation for a hanger with three y's balancing with 5.1?

• y = 5.1

• 3y = 6

• y + y + y = 5.1

• 3y = 5.1

What is the first step to find the value of x using a hanger?

• Subtract 1 from both sides

• Multiply both sides by 2

• Remove half of the x's

• Add more weight to the hanger