Examples with solutions for Variables and Algebraic Expressions: Applying the formula

Exercise #1

18x7+4x98x=? 18x-7+4x-9-8x=\text{?}

Video Solution

Step-by-Step Solution

To solve the exercise, we will reorder the numbers using the substitution property.

18x8x+4x79= 18x-8x+4x-7-9=

To continue, let's remember an important rule:

1. It is impossible to add or subtract numbers with variables.

That is, we cannot subtract 7 from 8X, for example...

We solve according to the order of arithmetic operations, from left to right:

18x8x=10x 18x-8x=10x 10x+4x=14x 10x+4x=14x 79=16 -7-9=-16 Remember, these two numbers cannot be added or subtracted, so the result is:

14x16 14x-16

Answer

14x16 14x-16

Exercise #2

8y+4534y45z=? 8y+45-34y-45z=\text{?}

Video Solution

Step-by-Step Solution

To solve this question, we need to remember that we can perform addition and subtraction operations when we have the same variable,
but we are limited when we have several different variables.
 

We can see in this exercise that we have three variables:
45 45 which has no variable
8y 8y and 34y 34y which both have the variable y y
and 45z 45z with the variable z z

Therefore, we can only operate with the y variable, since it's the only one that exists in more than one term.

Let's rearrange the exercise:

4534y+8y45z 45-34y+8y-45z

Let's combine the relevant terms with y y

4526y45z 45-26y-45z

We can see that this is similar to one of the other answers, with a small rearrangement of the terms:

26y+4545z -26y+45-45z

And since we have no possibility to perform additional operations - this is the solution!

Answer

26y+4545z -26y+45-45z

Exercise #3

7.34a+2.3+8a=? 7.3\cdot4a+2.3+8a=\text{?}

Video Solution

Step-by-Step Solution

It is important to remember that when we have numbers and variables, it is impossible to add or subtract them from each other.

We group the elements:

 

7.3×4a+2.3+8a= 7.3×4a + 2.3 + 8a =

29.2a + 2.3 + 8a = 

37.2a+2.3 37.2a + 2.3

 

And in this exercise, this is the solution!

You can continue looking for the value of a.

But in this case, there is no need.

Answer

37.2a+2.3 37.2a+2.3

Exercise #4

3x+4x+7+2=? 3x+4x+7+2=\text{?}

Video Solution

Answer

7x+9 7x+9

Exercise #5

3z+19z4z=? 3z+19z-4z=\text{?}

Video Solution

Answer

18z 18z

Exercise #6

35m+9n48m+52n=? 35m+9n-48m+52n=?

Video Solution

Answer

61n13m 61n-13m

Exercise #7

5a+3a+8b+10b=? 5a+3a+8b+10b=\text{?}

Video Solution

Answer

8a+18b 8a+18b

Exercise #8

7a+8b+4a+9b=? 7a+8b+4a+9b=\text{?}

Video Solution

Answer

11a+17b 11a+17b

Exercise #9

13a+14b+17c4a2b4b=? 13a+14b+17c-4a-2b-4b=\text{?}

Video Solution

Answer

9a+8b+17c 9a+8b+17c

Exercise #10

a+b+bc+9a+10b+3c=? a+b+bc+9a+10b+3c=\text{?}

Video Solution

Answer

10a+11b+(b+3)c 10a+11b+(b+3)c

Exercise #11

3.43.4a+2.6b7.5a=? 3.4-3.4a+2.6b-7.5a=\text{?}

Video Solution

Answer

3.410.9a+2.6b 3.4-10.9a+2.6b

Exercise #12

39.3:4a+5a+8.2+13z=? 39.3:4a+5a+8.2+13z=\text{?}

Video Solution

Answer

13z+8.2+9.825a+5a 13z+8.2+\frac{9.825}{a}+5a

Exercise #13

5.6x+7.9y+53xy+12.1x=? 5.6x+7.9y+53xy+12.1x=\text{?}

Video Solution

Answer

17.7x+53xy+7.9y 17.7x+53xy+7.9y

Exercise #14

7.8+3.5a80b7.8b+3.9a=? 7.8+3.5a-80b-7.8b+3.9a=\text{?}

Video Solution

Answer

7.8+7.4a87.8b 7.8+7.4a-87.8b

Exercise #15

14a+13x+24a+18+38=? \frac{1}{4}a+\frac{1}{3}x+\frac{2}{4}a+\frac{1}{8}+\frac{3}{8}=\text{?}

Video Solution

Answer

34a+13x+12 \frac{3}{4}a+\frac{1}{3}x+\frac{1}{2}

Exercise #16

38a+149b+119b+68a=? \frac{3}{8}a+\frac{14}{9}b+1\frac{1}{9}b+\frac{6}{8}a=\text{?}

Video Solution

Answer

118a+223b 1\frac{1}{8}a+2\frac{2}{3}b