Solving Equations by Simplifying Like Terms

πŸ†Practice solution of an equation using addition of like terms

Simplify the like terms in an equation involves combining the elements that belong to the same group. In other words: in all first-degree equations with one unknown, there are elements that belong to the group of unknowns (variables) and elements that belong to the group of numbers. The goal is to unite all the elements of each of the mentioned groups into respective sides to thus arrive at the result of the equation.

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Test yourself on solution of an equation using addition of like terms!

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\( x+x=8 \)

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Below, we provide you with some examples where we apply this method.

Example 1

X+2X=5+1 X+2X=5+1

In this equation, we can clearly see that the elements X X and 2X 2X belong to the group of unknowns, and therefore, we can combine them.

Conversely, the elements 5 5 and 1 1 belong to the group of numbers and thus can also be combined.Β 

3X=6 3X=6

X=2 X=2

The result of the equation is 2 2 .


Example 2

6Xβˆ’1=5X+5 6X-1=5X+5

In this equation, we can clearly see that the elements 6X 6X and 5X 5X belong to the group of variables, and therefore, we can combine them.

Conversely, the elements (βˆ’1) (-1) and 5 5 belong to the group of numbers, and thus they can also be combined.

6Xβˆ’5X=5+1 6X-5X=5+1

X=6 X=6

The result of the equation is 6 6 .


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Exercises on Equations by Simplifying Like Terms

Exercise 1

Assignment

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

Solution

We arrange the corresponding elements

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

We add accordingly

11a+8b+9b=? 11a+8b+9b=\text{?}

11a+17b 11a+17b

Answer

11a+17b 11a+17b


Exercise 2

Assignment:

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

Solution

We add the corresponding elements

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

7x+9 \text{7x+9}

Answer

7x+9 \text{7x+9}


Do you know what the answer is?

Exercise 3

Assignment

18xβˆ’7+4xβˆ’9βˆ’8x=? 18x-7+4x-9-8x=\text{?}

Solution

We input the corresponding elements

18x+4xβˆ’8xβˆ’7βˆ’9=? 18x+4x-8x-7-9=\text{?}

We solve accordingly

22xβˆ’8xβˆ’7βˆ’9=? 22x-8x-7-9=\text{?}

14xβˆ’7βˆ’9=? 14x-7-9=\text{?}

Answer

14xβˆ’16 14x-16


Exercise 4

Assignment

7.3β‹…4a+2.3+8a=? 7.3\cdot4a+2.3+8a=\text{?}

Solution

First, we solve the multiplication exercise

29.2a+2.3+8a= 29.2a+2.3+8a=

We arrange the terms accordingly

29.2a+8a+2.3= 29.2a+8a+2.3=

We add the terms accordingly

37.2a+2.3 37.2a+2.3

Answer

37.2a+2.3 37.2a+2.3


Check your understanding

Exercise 5

Assignment

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

Solution

We input the corresponding elements

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

We add accordingly

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

We convert the mixed number into an improper fraction

3+68a+149b+109b= \frac{3+6}{8}a+\frac{14}{9}b+\frac{10}{9}b=

We add accordingly

98a+14+109b= \frac{9}{8}a+\frac{14+10}{9}b=

98a+249b= \frac{9}{8}a+\frac{24}{9}b=

We convert the improper fractions into mixed numbers

118a+249b= 1\frac{1}{8}a+\frac{24}{9}b=

118a+269b 1\frac{1}{8}a+2\frac{6}{9}b

Answer

118a+269b 1\frac{1}{8}a+2\frac{6}{9}b


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