Solving Linear Equations and Word Problems

The video tutorial covers solving two-step equations, starting with basic examples and progressing to real-life word problems. It explains the process of isolating variables using inverse operations and checking solutions. The tutorial includes examples like 8x - 5 = 19, 1 - 9x = -80, and word problems involving taxi fares, submarine descent, and personal finances. Each problem is solved step-by-step, emphasizing the importance of understanding operations and verifying answers.

What is the first step in solving the equation 8x - 5 = 19?

• Multiply both sides by 8

• Subtract 5 from both sides

• Divide both sides by 8

• Add 5 to both sides

In the equation 1 - 9x = -80, what operation should be performed first?

• Subtract 1 from both sides

• Add 1 to both sides

• Divide both sides by 9

• Multiply both sides by 9

How do you isolate x in the equation -6 + x/4 = -5?

• Multiply both sides by 4

• Subtract 6 from both sides

• Add 6 to both sides

• Divide both sides by 4

What is the value of x in the equation x/(-4) + 8 = 5?

• x = 20

• x = 12

• x = -12

• x = -20

What is the inverse operation of division when solving equations?

• Addition

• Subtraction

• Division

• Multiplication

If Sally's taxi fare is $3 per mile and she gives a $7 tip, totaling $49, how many miles did she travel?

• 16 miles

• 10 miles

• 12 miles

• 14 miles

A submarine dives at 10 feet per minute from 214 feet below sea level to 464 feet. How long does it take?

• 30 minutes

• 25 minutes

• 20 minutes

• 35 minutes

In the equation -214 - 10x = -464, what is the first step to isolate x?

• Divide both sides by 10

• Multiply both sides by 10

• Subtract 214 from both sides

• Add 214 to both sides

Matilda spent half of her allowance and found $50, totaling $174. How much was her original allowance?

• $248

• $200

• $150

• $300

Diego splits his debt over three weeks with a $15 fee, spending $139 weekly. What was his total debt?

• $372

• $450

• $300

• $400