Solving Equations and Word Problems

This video tutorial covers seventh-grade math lesson 6.2 on one-step equations with rational coefficients. It begins with a review of one-step equations, emphasizing the use of inverse operations to isolate variables. The tutorial explains rational coefficients, including whole numbers, fractions, and decimals. Several examples demonstrate solving equations with rational numbers. The video also addresses translating word problems into mathematical equations and solving them, reinforcing the concepts taught.

What is the first step in solving a one-step equation?

• Multiply both sides by zero

• Use inverse operations to isolate the variable

• Subtract the variable from both sides

• Add the same number to both sides

Which of the following is NOT considered a rational coefficient?

• Whole numbers

• Fractions

• Decimals

• Irrational numbers

If you have the equation 3x = 27, what operation would you use to solve for x?

• Multiply both sides by 3

• Subtract 3 from both sides

• Divide both sides by 3

• Add 3 to both sides

In the equation x + 3.2 = -8, what is the value of x?

• -5.2

• -11.2

• -4.8

• -12.7

How do you handle a negative coefficient in a one-step equation?

• Add the coefficient to both sides

• Multiply both sides by the negative coefficient

• Divide both sides by the negative coefficient

• Subtract the coefficient from both sides

What is the vertical distance a diver travels if they start at -12.2 meters and stop at -4.55 meters?

• 7.65 meters

• 8.65 meters

• 6.65 meters

• 5.65 meters

When translating a word problem into an equation, what is the first step?

• Circle the numbers

• Underline the question

• Draw a diagram

• Solve the equation

If a temperature decreases by 3/4 degree per hour, how many hours will it take to decrease by 5 degrees?

• 8 hours

• 6.67 hours

• 7 hours

• 6 hours

What is the result of dividing 30 by 0.5?

• 45

• 60

• 15

• 30

In the equation -q/3.5 = 9.2, what is the value of q?

• -32.7

• -32.9

• -32.5

• -32.2