**Reasoning with properties from algebra worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on reasoning properties from algebra.

**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.

**Problem 1 :**

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

**Solution : **

**Given : **

7x - 2 = 4x + 13

**Subtract 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

**Problem 2 :**

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

**Solution : **

**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

**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 ?

**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 (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.

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

**Problem 4 :**

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

**Solution : **

**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)

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

(1) -----> AC = BD

After having gone through the stuff given above, we hope that the students would have understood "Reasoning with properties from algebra worksheet".

Apart from the stuff given above, if you want to know more about "Reasoning with properties from algebra", please click here

Apart from the stuff given on "Reasoning with properties from algebra worksheet", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**