Solving Equations for x

The video tutorial demonstrates solving two algebraic equations for x in terms of a and b. The first equation involves grouping x terms on one side and factoring out x, while the second equation requires distributing terms and rearranging to isolate x. The instructor guides through each step, emphasizing the importance of organizing terms and factoring to simplify the equations.

What is the initial equation that needs to be solved for x?

• ax - 3x = bx + 5

• ax + 3x = bx + 8

• ax + 3x = bx + 5

• ax + 3x = bx - 5

What operation is performed to move bx to the left-hand side of the equation?

• Subtracting bx from both sides

• Dividing both sides by bx

• Multiplying both sides by bx

• Adding bx to both sides

After grouping all x terms on the left, what is the next step to solve for x?

• Add 5 to both sides

• Factor out x from the left-hand side

• Multiply both sides by a

• Subtract 3 from both sides

What expression is x divided by to solve for it in the first equation?

• a + b - 3

• a + 3 + b

• a - 3 + b

• a + 3 - b

What is the new equation introduced in the second part of the video?

• a(5 - x) = bx + 8

• a(5 - x) = bx - 8

• a(5 + x) = bx - 8

• a(5 - x) = bx + 5

What is the first step in solving the new equation a(5 - x) = bx - 8?

• Factor out x from both sides

• Distribute a on the left-hand side

• Add bx to both sides

• Subtract 8 from both sides

What is the purpose of subtracting bx from both sides in the new equation?

• To eliminate bx from the equation

• To isolate x terms on one side

• To add more terms to the equation

• To simplify the equation

What operation is performed to eliminate negative signs in the equation?

• Subtract 1 from both sides

• Multiply both sides by -1

• Divide both sides by -1

• Add 1 to both sides

What expression is x divided by to solve for it in the second equation?

• a + 5

• a + b

• b - a

• a - b

What is the final expression for x in the second equation?

• 8 + 5a / a + b

• 8 - 5a / a + b

• 8 + 5a / a - b

• 8 + 5a / b - a