Solving Equations with Variables on Both Sides

This video tutorial covers solving equations with variables on both sides, including those with rational numbers. It provides step-by-step examples to solve for variables Y, K, and X, demonstrating techniques like distribution and using inverse operations. The tutorial also includes real-world applications, such as determining when two ponds will have the same depth and solving a perimeter problem involving a square and an equilateral triangle.

What is the first step when solving equations with variables on both sides?

• Check the solution

• Isolate the variable

• Distribute any terms if necessary

• Combine like terms on both sides

In the first example, why does the teacher prefer to collect variables on the side where the coefficient is greater?

• It makes the equation simpler

• It reduces calculation errors

• It avoids negative coefficients

• It is a standard rule

Tags

CCSS.8.EE.C.7B

What is the value of Y in the first example after solving the equation?

• 20

• 15

• 10

• 5

Tags

CCSS.7.EE.B.4A

In the second example, what is the common denominator used to rewrite 1/2 K and 1/4 K?

• 1/2

• 1/4

• 2/4

• 3/4

What is the final value of K in the second example?

• 24

• 12

• 48

• 36

Tags

CCSS.8.EE.C.7B

In the third example, what is the reciprocal of 1/7?

• 1/4

• 7

• 4

• 1/7

What happens when the variables cancel out on both sides of the equation?

• The equation has no solution

• The equation needs to be simplified further

• The equation has a unique solution

• The equation has infinite solutions

Tags

CCSS.8.EE.C.7A

In the application problem, what is the starting depth of Jackson's pond?

• 45 feet

• 1/2 foot

• 33 feet

• 1/4 foot

How many weeks will it take for Jackson's and Paul's ponds to have the same depth?

• 16 weeks

• 14 weeks

• 18 weeks

• 12 weeks

Tags

CCSS.8.EE.C.8C

What is the perimeter of a square with side length 2x - 2?

• 6x - 6

• 4x - 2

• 8x - 4

• 10x - 12

Tags

CCSS.7.EE.A.1