Expressions and Equations

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NEO Tue, Jan 25, 2022 08:21 AM UTC

This pdf gives us a clear view of what is Expressions and Equations. In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. For example, 3x² − 2xy + c is an algebraic expression

1. EXPRESSIONS and EQUATIONS
As you study mathematics, it will be very important to distinguish between an expression and an
equation. You solve an equation but simplify an expression.
Expression: an expression is a collection of math symbols with no equals sign.
The math symbols might include numbers, variables (letters), operation symbols ( +, - , *, /, or
^ ), and such grouping symbols as parentheses ( ), brackets [ ], or braces { }.
Some examples of expressions:
(notice that they do NOT equal anything).
(3x - 2) * 4 [ 23 - 2( x - 1)]
9x - 1
4x + 7
π(y) + 2eπι
We simplify expressions.
To simplify means to "do arithmetic, perform algebra" until there is nothing more to do.
Simplify the expression: 5(3x + 2) - 2(x + 1)
distribute: 5(3x) + 5(2) - 2(x) - 2(1)
multiply: 15x + 10 - 2x - 2
combine like terms: 15x - 2x + 10 - 2
the answer: 13x + 8
Notice that we have not tried to find what "x" equals.
There is no equals sign in the original problem.
Also see a related topic: order of operations

2. Equation: an equation is formed when two expressions are equal.
An equation has three parts to it:
The Left Side An Equals Sign The Right Side
(an expression) (another expression)
3x + 2 = 8
Some examples of equations:
7x - 25 = 2x + 15
2x - 1 = 3x + 2
5x + 4 1x - 3
sin2(x) + 2sin(x) + 1 = 0
To solve an equation means to use algebraic rules which allow you to find the value(s) for the
variable (the letter) which will make the original equation true.
solve: 3x - 2 = 1x + 6
subtract "1x" from each side: 3x -1x - 2 = 1x -1x + 6
2x - 2 = 0 + 6
add "2" to both sides: 2x - 2 + 2 = 6+2
2x = 8
divide both sides by 2: 2x = 8
2 2
the answer: x = 4
We have found what value of "x" will make the equation 3x - 2 = 1x + 6 true.
To check the solution, replace "x" by the "4" and see if a true statement is formed.
3x - 2 = 1x + 6
3(4) - 2 = 1(4) + 6
12 - 2 = 4 + 6
10 = 10
Ten equals ten is a "true" statement. The solution worked!

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