Solving Linear Equations with Variables on Both Sides

Maria, a mathematician, explains how to solve linear equations with variables on both sides. She demonstrates the process using an example equation, emphasizing the importance of balancing variables on one side and using inverse operations. Maria guides through each step, from subtracting like terms to dividing to find the solution, ensuring clarity in the process. The tutorial concludes with a recap of the method used to solve such equations.

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

• Isolate the variable on one side

• Multiply both sides by the same number

• Divide both sides by the same number

• Add the coefficients

Why is it recommended to eliminate the smaller coefficient first?

• To avoid fractions

• To avoid negative numbers

• To make the equation longer

• To make the equation more complex

What operation is used to eliminate the smaller coefficient in the equation 3x - 7 = 5x + 4?

• Addition

• Multiplication

• Subtraction

• Division

What happens when you subtract 3x from both sides of the equation 3x - 7 = 5x + 4?

• 3x is added to both sides

• 3x remains on both sides

• 3x is multiplied on both sides

• 3x cancels out on one side

After subtracting 3x from both sides, what is the resulting equation?

• 7 = 8x + 4

• -7 = 2x + 4

• 7 = 2x + 4

• -7 = 8x + 4

What is the next step after simplifying the equation to -7 = 2x + 4?

• Multiply both sides by 2

• Subtract 4 from both sides

• Add 4 to both sides

• Divide both sides by 2

What is the result of -7 - 4?

• -3

• 11

• -11

• 3

What is the final step to solve for x in the equation -11 = 2x?

• Subtract 2 from both sides

• Add 2 to both sides

• Multiply both sides by 2

• Divide both sides by 2

What is the value of x in the equation -11 = 2x?

• 5.5

• -5.5

• 11

• -11

How can -11/2 be expressed as a mixed number?

• -5 and 1/2

• 11 and 1/2

• 5 and 1/2

• -11 and 1/2