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How to Solve an Algebraic Expression
An algebraic expression is a mathematical phrase that contains numbers and/or variables. Though it cannot be solved because it does not contain an equals sign (=), it can be simplified. You can, however, solve algebraic equations, which contain algebraic expressions separated by an equals sign. If you want to know how to master this mathematical concept, then see Step 1 to get started.
Part One of Two:
Understanding the Basics
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1
Understand the difference between an algebraic expression and an algebraic equation. An algebraic expression is a mathematical phrase that can contain numbers and/or variables. It does not contain an equals sign and cannot be solved. An algebraic equation, however, can be solved, and does include a series of algebraic expressions separated by an equals sign. Here are some examples:
Algebraic expression: 4x + 2
Algebraic equation: 4x + 2 = 100
2
Know how to combine like terms. Combining like terms just means adding up (or subtracting) the terms of the same degree. This means that all x2 terms can be combined with other x2 terms, that all x3 terms can be combined with x3 terms, and that all constants, numbers that are not attached to variables, such as 8 or 5, can be added up, or combined, as well. Here's an example:
3x2 + 5 + 4x3 - x2 + 2x3 + 9 =
3x2 - x2 + 4x3 + 2x3 + 5 + 9 =
2x2 + 6x3 + 14
3
Know how to factor a number. If you're working with an algebraic equation, which means there is an expression on either side of an equals sign, then you can simplify it by factoring out a common term. Look at the coefficients of all of the terms (the numbers before the variables, or the constants) and see if there is a number that you can "factor out" by dividing each term by that number. If you can do this, then you have simplified the equation and are on your way to solving it. Here's how:
3x + 15 = 9x + 30
You can see that each coefficient can be divisible by 3. Just "factor out" the number 3 by dividing each term by 3 to get your simplified equation.
3x/3 + 15/3 = 9x/3 + 30/3 =
x + 5 = 3x + 10
4
Know the order of operations. The order of operations, also known by the acronym PEMDAS, explains the order in which you should perform different mathematical operations. The order is: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Here's an example of how the order of operations works:
(3 + 5)2 x 10 + 4
First, follow P, the operation in the parentheses:
= (8)2 x 10 + 4
Then, follow E, the operation of the exponent:
= 64 x 10 + 4
Next, do multiplication:
= 640 + 4
And last, do addition:
= 644
5
Learn how to isolate a variable. If you're solving an algebraic equation, then your goal is to get the variable, often known as x, on one side of the equation, while placing the constant terms on the other side of the equation. You can isolate x by division, multiplication, addition, subtraction, finding the square root, or other operations. Once you've isolated x, you can solve for it. Here's how:
5x + 15 = 65 =
5x/5 + 15/5 = 65/5 =
x + 3 = 13 =
x = 10
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Part Two of Two:
Solve an Algebraic Equation
Edit
An algebraic expression is a mathematical phrase that contains numbers and/or variables. Though it cannot be solved because it does not contain an equals sign (=), it can be simplified. You can, however, solve algebraic equations, which contain algebraic expressions separated by an equals sign. If you want to know how to master this mathematical concept, then see Step 1 to get started.
Part One of Two:
Understanding the Basics
Edit
1
Understand the difference between an algebraic expression and an algebraic equation. An algebraic expression is a mathematical phrase that can contain numbers and/or variables. It does not contain an equals sign and cannot be solved. An algebraic equation, however, can be solved, and does include a series of algebraic expressions separated by an equals sign. Here are some examples:
Algebraic expression: 4x + 2
Algebraic equation: 4x + 2 = 100
2
Know how to combine like terms. Combining like terms just means adding up (or subtracting) the terms of the same degree. This means that all x2 terms can be combined with other x2 terms, that all x3 terms can be combined with x3 terms, and that all constants, numbers that are not attached to variables, such as 8 or 5, can be added up, or combined, as well. Here's an example:
3x2 + 5 + 4x3 - x2 + 2x3 + 9 =
3x2 - x2 + 4x3 + 2x3 + 5 + 9 =
2x2 + 6x3 + 14
3
Know how to factor a number. If you're working with an algebraic equation, which means there is an expression on either side of an equals sign, then you can simplify it by factoring out a common term. Look at the coefficients of all of the terms (the numbers before the variables, or the constants) and see if there is a number that you can "factor out" by dividing each term by that number. If you can do this, then you have simplified the equation and are on your way to solving it. Here's how:
3x + 15 = 9x + 30
You can see that each coefficient can be divisible by 3. Just "factor out" the number 3 by dividing each term by 3 to get your simplified equation.
3x/3 + 15/3 = 9x/3 + 30/3 =
x + 5 = 3x + 10
4
Know the order of operations. The order of operations, also known by the acronym PEMDAS, explains the order in which you should perform different mathematical operations. The order is: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Here's an example of how the order of operations works:
(3 + 5)2 x 10 + 4
First, follow P, the operation in the parentheses:
= (8)2 x 10 + 4
Then, follow E, the operation of the exponent:
= 64 x 10 + 4
Next, do multiplication:
= 640 + 4
And last, do addition:
= 644
5
Learn how to isolate a variable. If you're solving an algebraic equation, then your goal is to get the variable, often known as x, on one side of the equation, while placing the constant terms on the other side of the equation. You can isolate x by division, multiplication, addition, subtraction, finding the square root, or other operations. Once you've isolated x, you can solve for it. Here's how:
5x + 15 = 65 =
5x/5 + 15/5 = 65/5 =
x + 3 = 13 =
x = 10
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Part Two of Two:
Solve an Algebraic Equation
Edit
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1. (x + 3)/6 = 2/3. First, cross multiply to get rid of the fraction. ...
2. (x + 3) x 3 = 2 x 6 =
3. 3x + 9 = 12. Now, combine like terms. ...
4. 3x + 9 - 9 = 12 - 9 =3x = 3. Isolate the variable, x, by dividing both sides by 3 and you've got your answer.
4.
3x/3 = 3/3 =x =1.
2. (x + 3) x 3 = 2 x 6 =
3. 3x + 9 = 12. Now, combine like terms. ...
4. 3x + 9 - 9 = 12 - 9 =3x = 3. Isolate the variable, x, by dividing both sides by 3 and you've got your answer.
4.
3x/3 = 3/3 =x =1.
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