Angle Relationships and Linear Equations

This video tutorial covers various mathematical problems and concepts for seventh-grade students. It begins with solving for unknown angles using equations, followed by finding angle values with perpendicular lines. The tutorial then explains complementary angles and how to solve inequalities. It includes practical problems like calculating time and speed in a race and solving a distance walked problem. Finally, it addresses identifying equivalent expressions using the distributive property.

If angle DCE measures 148 degrees and the sum of angles at point C is 180 degrees, what is the value of x?

• 32 degrees

• 64 degrees

• 148 degrees

• 16 degrees

When line L is perpendicular to line M, and W is 42 degrees, what is the value of x if 19 + x + W = 90?

• 19 degrees

• 29 degrees

• 42 degrees

• 61 degrees

If two angles are complementary and one measures 30 degrees, what is the measure of the other angle?

• 120 degrees

• 60 degrees

• 30 degrees

• 90 degrees

In the inequality -6x + 3 > -24, what is the solution for x?

• x < 4.5

• x > 4.5

• x = 4.5

• x < -4.5

What is the solution for x in the inequality -8x > -36?

• x > 4.5

• x < -4.5

• x < 4.5

• x = 4.5

How long does it take to run the entire 5 km race if 2/3 of it takes 21 minutes?

• 31.5 minutes

• 10.5 minutes

• 42 minutes

• 21 minutes

How many minutes does it take to run one kilometer at a constant speed if the entire race takes 31.5 minutes?

• 5 minutes

• 6.3 minutes

• 7 minutes

• 10.5 minutes

If Jada walked 4 more miles than Elena, and Lynn walked 2 more miles than Jada, how many miles did Elena walk if they walked a total of 37 miles?

• 9 miles

• 13 miles

• 15 miles

• 37 miles

Which expression is equivalent to -36x + 54y - 90?

• -36x + 108y - 180

• -36x + 54y - 90

• -36x - 54y + 90

• -36x + 54y + 90

After using the distributive property, which expression is correct for -18 times all three terms?

• -36x + 108y - 180

• -36x + 54y - 90

• -36x + 54y + 90

• -36x - 54y + 90