Combining Like Terms
What are Like Terms?
Like terms are variable terms that differ only in their coefficients.
What is a term?
A term is product or quotient involving numbers
and/or variables. Terms are separated in expressions by addition or subtraction. What is a Coefficient?
A coefficient is the numeral in a variable term usually
preceding the variable. 
What is a numerical term?
Numerical terms  numerals. All rational numerical
terms can be combined. What are Variable terms?
Variable terms are terms with variables and coefficients.
Only like variable terms can be combined. What are Irrational Numbers
Irrational numbers can not be combined with rational numbers.

Combining Like Terms
A frequentlyused procedure in algebra is the process of combining like terms. This is a way to "cleanup" an equation and make it much easier to solve. In case you've forgotten, a term is each single part of an expression. For example, in the expression 4x + 3 + 7y, there are three terms: 4x, 3, and 7y. The number 4 is not a term, but rather a factor of the term 4x.
Let's say we are given the equation below. It looks very complicated, but if we look carefully, everything is either a constant (a number), or the variable x with a coefficient (4x). By the way, a coefficient is the number by which a variable is being multiplied (the 4 in 4x is the coefficient).
The "like terms" in the equation above are ones that have the same variable. All constants are like terms as well. This means that the 15, 10, 6, and 2 are all one set of like terms, and the other is 4x, 3x, 5x, and 3x. To combine them is pretty easy, you just add them together and make sure that they are all on the same side of the equation. First, we will combine all like terms on each side of the equation:
Since the 15 and 10 are both constants we combine them to get 25. The 4x and 3x each have the same variable (x), so we can add them to get 1x. Doing the same on the other side we arrive at 25 + 1x = 4 + 8x. The process is still not finished, however. There are still some like terms, but they are on opposite sides of the equal sign. Since we can do the same thing to both sides we just subtract 4 from each side and subtract 1x from each side:
Now it's just a simple process of dividing by seven on each side:
And we arrive at our answer of x=3. Combining like terms enabled you to take that huge mess of an equation and make it into something much more obvious.
Let's say we are given the equation below. It looks very complicated, but if we look carefully, everything is either a constant (a number), or the variable x with a coefficient (4x). By the way, a coefficient is the number by which a variable is being multiplied (the 4 in 4x is the coefficient).
The "like terms" in the equation above are ones that have the same variable. All constants are like terms as well. This means that the 15, 10, 6, and 2 are all one set of like terms, and the other is 4x, 3x, 5x, and 3x. To combine them is pretty easy, you just add them together and make sure that they are all on the same side of the equation. First, we will combine all like terms on each side of the equation:
Since the 15 and 10 are both constants we combine them to get 25. The 4x and 3x each have the same variable (x), so we can add them to get 1x. Doing the same on the other side we arrive at 25 + 1x = 4 + 8x. The process is still not finished, however. There are still some like terms, but they are on opposite sides of the equal sign. Since we can do the same thing to both sides we just subtract 4 from each side and subtract 1x from each side:
Now it's just a simple process of dividing by seven on each side:
And we arrive at our answer of x=3. Combining like terms enabled you to take that huge mess of an equation and make it into something much more obvious.
Combining Like Terms
You will be able to combine like terms to simplify expressions.
Solve for x:
Solve a onestep equation for the value of an unknown variable. 1) x – 5 = 7 2) 5x = 15 3) x + 9 = 5 4) 6x = 42 Solve a twostep equation for the value of an unknown variable. 5) 2x + 1 = 13 6) 4x – 3 = 23 7) 4x + 9 = 17 8) 12 x – 10 = 14 Apply the distributive property to simplify expressions. 9) 5(2x + 12) 10) 3(7x + 2y – 4) 11) 6x(3x + 8) 12) x(x + y – z) Combine like terms to simplify expressions. 13) 5x + 9x – 12x 14) 8x + 7 + 6x + 9 15) 4x^2 – 10x + 8 – 3x – 1 16) 5 – 3y + x + 7y + x + 13 – 2 Simplify general expressions, and explain what it means to “simplify” an expression. 17) 18 – 3 + 2(1 + 5) 18) 4(7x – 5) 19) 9x – 2y – 8 + 4x + 2 20) 3(2x – 8) + x – 4•5 Simplify and solve multistep linear equations in one variable. 21) 7(x + 2) = 49 22) 8x + 1 + 2x = 59 23) 3x + 3(4x – 5) = 21 24) 3(2x – 5) + 4(x – 2) = 12 
Linear: In a straight line.
Expression: A number or a group of numbers written with operations signs.Numbers, symbols and operators (such as + and ×) grouped together that show the value of something. Example 2×3 is an expression Positive numbers: The numbers to the right of zero on the number line. Negative numbers: The numbers to the left of zero on the number line. Simplify: To carry out the operations to find the value. Solve: To find the solution to an equation. 
Equation: A statement that two expressions are equal.
Term: The part of an equation separated by an addition (+) or a minus () sign. Like Terms: Numbers or terms that have the same variable with the same exponent. Variable: A letter that represents a number. Distributive Property: To multiply a sum or difference by a number, multiply each number of the sum or difference. 