REASONING WITH PROPERTIES FROM ALGEBRA WORKSHEET

Problem 1 :

Solve 7x - 2  =  4x + 9 and write a reason for each step.

Problem 2 :

Solve 52y - 3(12 + 9y)  =  64 and write a reason for each step.

Problem 3 :

When we do exercise every day, we should find our target heart rate. This is the rate at which we achieve an effective workout while not placing too much strain on our heart. Our target heart rate r (in beats per minute) can be determined from our age a (in years) using the equation a = 220 - 10r/7.

(i) Solve the formula for r and write a reason for each step.

(ii) Use the result to find the target heart rate for a 16 year old.

(iii) Find the target heart rate for the following ages :

20, 30, 40, 50 and 60

What happens to the target heart rate as a person gets older?

Problem 4 :

In the diagram above, AB  =  CD. Prove AC  =  BD.

1. Answer :

Given :

7x - 2  =  4x + 13

Subtraction property of equality :

Subtract 4x from each side.

3x - 2  =  13

Addition property of equality :

Add 2 to each side.

3x  =  15

Division property of equality :

Divide both sides by 2.

x  =  5

2. Answer :

Given :

52y - 3(12 + 9y)  =  64

Distributive Property :

Distribute 3 to 12 and 9y.

52y - 36 - 27y  =  64

Simplify :

25y - 36  =  64

Addition property of equality :

Add 36 to each side.

25y  =  100

Division property of equality :

Divide both sides by 25.

y  =  4

3. Answer :

Solution (i) :

Given :

a  =  220 - 10r/7

Addition property of equality :

Add 10r/7 to each side.

a + 10r/7  =  220

Subtraction property of equality :

Subtract a from each side.

10r/7  =  220 - a

Multiplication property of equality :

Multiply both sides by 7/10.

r  =  7/10 ⋅ (220 - a)

Solution (ii) :

To find the target heart rate for a 16 year old, substitute a = 16.

r  =  7/10 ⋅ (220 - 16)

Simplify :

r  =  7/10 ⋅ 204

r  =  1428 / 10

r  =  142.8

The target hear rate for a 16 year old is about 142.8 beats per minute.

Solution (iii) :

The table given below shows the heart rate for ages 20, 30, 40, 50 and 60.

Solution (iv) :

From the above table, it is clear that the target heart rate appears to decrease as a person gets older.

4. Answer :

Given :

AB  =  CD

Addition property of equality :

Add BC to each side.

AB + BC  =  CD + BC

  AB + BC  =  BC + CD ------(1)

By segment addition postulate, we have

AC  =  AB + BC -----(2)

BD  =  BC + CD -----(3)

Substitution property of equality :

Substitute (2) and (3) in (1).

(1) -----> AC  =  BD

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.