Solving Equations with Variables on Both Sides

This video tutorial covers solving equations with variables on both sides, focusing on simplifying expressions, combining like terms, and moving variables to one side. It includes seven examples, each demonstrating different aspects of solving equations, such as handling fractions and applying these skills to geometry problems like finding the perimeter.

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

• Simplify the constants first

• Isolate the variable immediately

• Move all variables to one side

• Combine like terms on each side

In solving equations with variables on both sides, why is it important to simplify each side first?

• To eliminate all variables

• To make the equation shorter

• To identify the variables

• To combine like terms and simplify the solving process

How do you simplify the expression 11x - 2x?

• 13x

• 9x

• 11x^2 - 2x^2

• -9x

What is the result of subtracting 2x from both sides of the equation 9x + 2 = 16 + 2x?

• 7x = 14

• 11x + 2 = 16

• 7x + 2 = 16

• 9x = 18

After simplifying both sides of an equation, what is the next step?

• Subtract the largest variable from the equation

• Move variables to the same side

• Combine all constants

• Divide both sides by the coefficient

What is the solution to the equation 7x - 15 = 41?

• x = 8

• x = 6

• x = 56

• x = 7

How do you solve an equation with a fraction coefficient, like 5/3x = 15?

• Subtract 5/3 from both sides

• Add 5/3 to both sides

• Multiply both sides by 3/5

• Divide both sides by 5/3

What is the perimeter equation for a triangle with sides 3x, 9, and 6?

• 3x + 18

• 9x + 15

• 3x + 15

• 3x + 9 + 6

If the perimeters of a triangle and a rectangle are equal, and the triangle's perimeter is 3x + 18, what is the first step to find x?

• Subtract 18 from 3x

• Divide the triangle's perimeter by 2

• Multiply 3x by 18

• Set 3x + 18 equal to the rectangle's perimeter

What is the solution for x when the perimeter of the rectangle is 4x + 10 and it's equal to the triangle's perimeter of 3x + 18?

• x = 4

• x = 28

• x = 10

• x = 8