Math linear equations in one variable
Answers
Linear Equation
An equation that can be written in the form
ax + b = c
where a, b, and c are constants
Note that the exponent ( definition found in Tutorial 4:
Operations on Real Numbers) on the variable of a linear
equation is always 1.
The following is an example of a linear equation: 3x - 4 =
5
Solution
A value, such that, when you replace the variable with it,
it makes the equation true.
(the left side comes out equal to the right side)
Solution Set
Set of all solutions
Example 1: Determine if any of the following
values for x are solutions to the given equation.
3x - 4 = 5 ; x = 3, 5.
Checking 3
3x - 4 = 5
3(3) - 4 = 5
9 - 4 = 5
5 = 5
True 3 is a solution
Checking 5
3 x - 4 = 5
3(5) - 4 = 5
15 - 4 = 5
11 = 5
False 5 is not a solution
Solving a Linear Equation
in General
Get the variable you are solving for alone on one side and
everything else on the other side using INVERSE
operations.
The following will give us the tools that we need to solve
linear equations.
Addition and Subtraction Properties of Equality
If a = b, then a + c = b + c
If a = b, then a - c = b - c
In other words, if two expressions are equal to each
other and you add or subtract the exact same thing to
both sides, the two sides will remain equal.
Note that addition and subtraction are inverse operations
of each other. For example, if you have a number that is
being added that you need to move to the other side of
the equation, then you would subtract it from both sides of
that equation.
Example 2: Solve for the variable. x - 5 =
2.
x - 5 = 2
x - 5 + 5 = 2 + 5
x = 7
*Inverse of sub. 5 is add. 5
Note that if you put 7 back in for x in the original problem
you will see that 7 is the solution to our problem.
Example 3: Solve for the variable. y + 4
= -7.
y + 4 = -7
y + 4 - 4 = -7 - 4
y = -11
*Inverse of add. 4 is sub. 4
Note that if you put -11 back in for y in the original
problem you will see that -11 is the solution we are
looking for .
Multiplication and Division Properties of Equality
If a = b, then a(c) = b(c)
If a = b, then a/c = b/c where c is not equal to 0.
Answer:
Two expressions set equal to each other
Linear Equation
An equation that can be written in the form
ax + b = c
where a, b, and c are constants
Note that the exponent ( definition found in Tutorial 4:
Operations on Real Numbers) on the variable of a linear
equation is always 1.
The following is an example of a linear equation: 3x - 4 =
5
Solution
A value, such that, when you replace the variable with it,
it makes the equation true.
(the left side comes out equal to the right side)
Solution Set
Set of all solutions
Example 1: Determine if any of the following
values for x are solutions to the given equation.
3x - 4 = 5 ; x = 3, 5.
Checking 3
3x - 4 = 5
3(3) - 4 = 5
9 - 4 = 5
5 = 5
True 3 is a solution
Checking 5
3 x - 4 = 5
3(5) - 4 = 5
15 - 4 = 5
11 = 5
False 5 is not a solution
Solving a Linear Equation
in General
Get the variable you are solving for alone on one side and
everything else on the other side using INVERSE
operations.
The following will give us the tools that we need to solve
linear equations.
Addition and Subtraction Properties of Equality
If a = b, then a + c = b + c
If a = b, then a - c = b - c
In other words, if two expressions are equal to each
other and you add or subtract the exact same thing to
both sides, the two sides will remain equal.
Note that addition and subtraction are inverse operations
of each other. For example, if you have a number that is
being added that you need to move to the other side of
the equation, then you would subtract it from both sides of
that equation.
Example 2: Solve for the variable. x - 5 =
2.
x - 5 = 2
x - 5 + 5 = 2 + 5
x = 7
*Inverse of sub. 5 is add. 5
Note that if you put 7 back in for x in the original problem
you will see that 7 is the solution to our problem.
Example 3: Solve for the variable. y + 4
= -7.
y + 4 = -7
y + 4 - 4 = -7 - 4
y = -11
*Inverse of add. 4 is sub. 4
Note that if you put -11 back in for y in the original
problem you will see that -11 is the solution we are
looking for .
Multiplication and Division Properties of Equality
If a = b, then a(c) = b(c)
If a = b, then a/c = b/c where c is not equal to 0.