Solving Equations with Variables on Both Sides

The video tutorial covers solving equations with variables on both sides. It begins with an introduction to the concept, followed by multiple examples demonstrating different methods and scenarios. Each example is solved step-by-step, and the solutions are checked using substitution. The tutorial emphasizes understanding the process and encourages students to practice independently.

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

• Divide both sides by the same number

• Get the variables together on one side

• Add the constants on both sides

• Multiply both sides by the same number

In the equation 10x - 19 = 6x + 19, what operation is performed to move 6x to the left side?

• Divide both sides by 6

• Multiply both sides by 6

• Subtract 6x from both sides

• Add 6x to both sides

What is the value of x in the equation 10x - 19 = 6x + 19?

• 11.5

• 8.5

• 9.5

• 10.5

Why is it important to check your solution after solving an equation?

• To find any possible errors in the constants

• To simplify the equation further

• To verify the solution satisfies the original equation

• To ensure the solution is a whole number

In the second example, why shouldn't we move 17x to the right side?

• Because it is a negative term

• Because it would leave the left side empty

• Because it is a constant

• Because it is already simplified

What is the value of x in the equation 17x - 11x = 78?

• 15

• 12

• 13

• 14

In the third example, what is the result of subtracting x from both sides of the equation?

• 12 = 5x + 47

• 12 = 8x + 47

• 12 = 6x + 47

• 12 = 7x + 47

What is the value of x in the equation 7x + 47 = 12?

• -7

• -6

• -5

• -4

In the fourth example, what is the decimal equivalent of 1/2?

• 0.2

• 0.3

• 0.4

• 0.5

What is the value of x in the final example after combining like terms and solving?

• -6

• -7

• -9

• -8