Solving Equations by Simplifying Like Terms

$X+2X=5+1$

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

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

$3X=6$

$X=2$

The result of the equation is $2$.

$6X-1=5X+5$

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

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

$6X-5X=5+1$

$X=6$

The result of the equation is $6$.

Assignment

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

Solution

We arrange the corresponding elements

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

We add accordingly

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

$11a+17b$

Answer

$11a+17b$

Assignment:

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

Solution

We add the corresponding elements

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

$\text{7x+9}$

Answer

$\text{7x+9}$

Assignment

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

Solution

We input the corresponding elements

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

We solve accordingly

$22x-8x-7-9=\text{?}$

$14x-7-9=\text{?}$

Answer

$14x-16$

Assignment

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

Solution

First, we solve the multiplication exercise

$29.2a+2.3+8a=$

We arrange the terms accordingly

$29.2a+8a+2.3=$

We add the terms accordingly

$37.2a+2.3$

Answer

$37.2a+2.3$

Assignment

$\frac{3}{8}a+\frac{14}{9}b+1\frac{1}{9}b+\frac{6}{8}a=\text{?}$

Solution

We input the corresponding elements

$\frac{3}{8}a+\frac{6}{8}a+\frac{14}{9}b+1\frac{1}{9}b=$

We add accordingly

$\frac{3+6}{8}a+\frac{14}{9}b+1\frac{1}{9}b=$

We convert the mixed number into an improper fraction

$\frac{3+6}{8}a+\frac{14}{9}b+\frac{10}{9}b=$

We add accordingly

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

$\frac{9}{8}a+\frac{24}{9}b=$

We convert the improper fractions into mixed numbers

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

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

Answer

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