Solving Linear Equations and Inequalities

The video tutorial covers solving equations with integers, focusing on working backwards to isolate variables. It explains solving equations involving addition, subtraction, multiplication, and division. The tutorial also includes a word problem about temperature, demonstrating how to set up and solve an equation. The importance of checking solutions is emphasized throughout.

What is the first step in solving an equation with integers?

• Divide both sides by the same number

• Work backwards by doing the opposite operation

• Multiply both sides by the same number

• Add the same number to both sides

If you have the equation p + 23 = 12, what operation should you perform to isolate p?

• Subtract 23 from both sides

• Add 23 to both sides

• Divide both sides by 23

• Multiply both sides by 23

In the equation t - 16 = -4, what is the value of t?

• -12

• 20

• 12

• -20

What is the result of dividing -30 by 5 in the equation 5m = -30?

• -6

• -5

• 6

• 5

In the equation p / -4 = -3, what is the value of p?

• 12

• -12

• -3

• 3

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

• To change the variable

• To verify the solution satisfies the original equation

• To make the equation more complex

• To ensure the solution is positive

What is the result of substituting m = -6 into the equation 5m = -30?

• 5 times 6 equals -30

• 5 times 6 equals 30

• 5 times -6 equals -30

• 5 times -6 equals 30

In the context of the temperature problem, what does the equation y + 12 = 45 represent?

• Today's temperature minus 12 equals yesterday's temperature

• Today's temperature is 12 degrees

• Yesterday's temperature is 45 degrees

• Yesterday's temperature plus 12 equals today's temperature

If today's temperature is 45 degrees and it is 12 degrees warmer than yesterday, what was yesterday's temperature?

• 33 degrees

• 57 degrees

• 45 degrees

• 12 degrees

How do you verify that the solution to the temperature problem is correct?

• By subtracting 12 from today's temperature

• By adding 12 to today's temperature

• By checking if yesterday's temperature plus 12 equals today's temperature

• By dividing today's temperature by 12