Solving Linear Equations and Inequalities

The video tutorial covers solving three-step algebraic equations by isolating variables on one side. The instructor demonstrates two examples, emphasizing the importance of keeping track of signs and checking solutions. The first example involves subtracting 2x from both sides, simplifying to a two-step equation, and verifying the solution. The second example also involves subtracting 2x, handling negative numbers, and verifying the solution. The tutorial aims to build confidence in solving similar algebraic problems.

What is the primary goal when solving a three-step equation?

• To make both sides of the equation equal

• To isolate the variable on one side

• To eliminate all numbers from the equation

• To multiply all terms by zero

What is the first step in solving the equation 5x - 2x - 3 = 12?

• Add 3 to both sides

• Subtract 2x from both sides

• Divide both sides by 5

• Multiply both sides by 2

After simplifying 5x - 2x - 3 = 12, what is the resulting equation?

• 5x - 3 = 12

• 3x - 3 = 12

• 3x + 3 = 12

• 5x + 3 = 12

What is the value of x in the equation 3x - 3 = 12?

• x = 6

• x = 5

• x = 4

• x = 3

How do you verify the solution x = 5 in the equation 5x - 3 = 12?

• Multiply both sides by 5

• Subtract 5 from both sides

• Substitute x = 5 into the original equation

• Add 5 to both sides

In the second problem, why might you choose to subtract 2x instead of 6x?

• To eliminate all x terms

• To keep the number of x terms positive

• To make the equation easier to read

• To make the equation more complex

What is the equation after subtracting 2x from both sides in the second problem?

• 4x - 7 = -21

• 6x + 7 = -21

• 6x - 7 = -21

• 4x + 7 = -21

What is the next step after obtaining 4x + 7 = -21?

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply both sides by 4

• Divide both sides by 4

What is the value of x in the equation 4x = -28?

• x = -4

• x = -5

• x = -6

• x = -7

How do you verify the solution x = -7 in the second problem?

• Substitute x = -7 into the original equation

• Subtract -7 from both sides

• Add -7 to both sides

• Multiply both sides by -7