😉 7th Grade, Unit 6, Lesson 2 'Reasoning about Contexts with Tape Diagrams (Part 1)' IM Math

😉 7th Grade, Unit 6, Lesson 2 "Reasoning about Contexts with Tape Diagrams (Part 1)" Illustrative Mathematics Practice Problems. Review and Tutorial. Search #762math to find this lesson fast!. Support for teachers and parents, This math tutorial is on 7th Grade Illustrative Math: Unit 6, Lesson 2 "Reasoning about Contexts with Tape Diagrams" (Part 1).

IM Math 7.6.2. and OUR Math 7.6.2. "Reasoning about Contexts with Tape Diagrams (Part 1)" Practice Problems

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[illustrativetutor]

Here is a peak at the 7th Grade, Unit 7, Lesson 5 Tutorial.
1) 180 - 148 = 32
32 divided by 2 = 16
Each of the two unknown angles are 16 degrees.

2) Line L and M form a 90 degree angle.
180 degrees - 138 degrees = 42 degrees which is also the angle for angle w.
90 - 19 - 42 = 29 which is also the angle for x.
Answer: w = 42 degrees, and x = 29 degrees.

3) Yes, we can find the measure of the other angle if we know that two angles are complementary and the measure of one of them.
Complementary angles are two angles whose sum is 90 degrees. So, if we know the measure of one angle, we can subtract it from 90 degrees to find the measure of the other angle.

Here is an example. If we know that one angle is 30 degrees and the angles are complementary, we can subtract 30 degrees from 90 degrees to get the measure of the other angle.
90 degrees - 30 degrees = 60 degrees
Therefore, the measure of the other angle is 60 degrees (for my example problem).

4) A. Starting with -24 > -6(x - 0.5), we can simplify by first distributing -6:
-24 > -6x + 3
Then, subtracting 3 from both sides:
-21 > -6x
Finally, dividing both sides by -6 (and remembering to flip the inequality since we are dividing by a negative number), we get:
x < 3.5
Therefore, the solution is represented by x < 3.5.

B. Starting with -8x + 6 > -30, we can first subtract 6 from both sides:
-8x > -36
Then, dividing both sides by -8 (and flipping the inequality again), we get:
x < 4.5
Therefore, the solution is represented by x < 4.5.

C. Starting with -2(x + 3.2) < -15.4, we can first distribute -2:
-2x - 6.4 < -15.4
Then, adding 6.4 to both sides:
-2x < -9
Finally, dividing both sides by -2 (and flipping the inequality again), we get:
x > 4.5
Therefore, the solution is represented by x > 4.5 .

5) A. If 2/3 of 5 kilometers takes 21 minutes, then we can use proportionality to find how long 3/3 of 5 kilometers will take.
We can set up the proportion:
2/3 of 5 km / 21 minutes = 3/3 of 5 km / x minutes
Simplifying this, we get:
(2/3) * 5 km * x = (3/3) * 5 km * 21 minutes
10x/3 = 105
Solving for x:
x = (105 * 3)/10
x = 31.5 minutes
Therefore, 3/3 of 5 kilometers will take 31.5 minutes.

B) B. 31.5 divided by 5 + 6.1. So one km would take 6.1 minutes.

6) Let's start by using algebra to solve the problem.
Let x be the number of miles Elena walked.
Then, Jada walked 4 more miles, so Jada walked x + 4 miles.
Lin walked 2 more miles than Jada, so Lin walked (x + 4) + 2 miles = x + 6 miles.
The total distance walked by all three is 37 miles:
x + (x + 4) + (x + 6) = 37
Simplifying and solving for x:
3x + 10 = 37
3x = 27
x = 9
So Elena walked 9 miles, Jada walked 9 + 4 = 13 miles, and Lin walked 13 + 2 = 15 miles.
Therefore, Elena walked 9 miles, Jada walked 13 miles, and Lin walked 15 miles.

7) To check which expressions are equivalent to -36x + 54y - 90, we can simplify each expression and see which ones result in the same expression as -36x + 54y - 90.

A. -9(4x - 6y - 10)
Distributing the -9:
-36x + 54y + 90
This is not equivalent to -36x + 54y - 90, so A is not equivalent.

B. -18(2x - 3y + 5)
Distributing the -18:
-36x + 54y - 90
This is equivalent to -36x + 54y - 90, so B is equivalent.

C. -6(6x + 9y - 15)
Distributing the -6:
-36x - 54y + 90
This is not equivalent to -36x + 54y - 90, so C is not equivalent.

D. 18(-2x + 3y - 5)
Distributing the 18:
-36x + 54y - 90
This is equivalent to -36x + 54y - 90, so D is equivalent.

E. -2(18x - 27y + 45)
Distributing the -2:
-36x + 54y - 90
This is equivalent to -36x + 54y - 90, so E is equivalent.

F. 2(-18x + 54y - 90)
Distributing the 2:
-36x + 108y - 180
This is not equivalent to -36x + 54y - 90, so F is not equivalent.
Therefore, the expressions that are equivalent to -36x + 54y - 90 are B, D, and E.

[Aviaion]

Are you sure for question number 2 because E says that they spent 87$ on 4 tickets so that’s already 87 without the 39