Transcript Lesson_7_Kling_1SolveLinEq1va

Solving linear equations

Review the properties of equality

Equations that involve simplification

Equations containing fractions

A general strategy for solving linear
equations
Solving linear equations

Review the properties of equality

Equations that involve simplification

Equations containing fractions

A general strategy for solving linear
equations
The properties of equality
The reflexive property of equality
a=a
The symmetric property of equality
a = b if and only if b = a
The transitive property of equality
If a = b and b = c, then a = c.
The properties of equality
The same real number, or algebraic
The addition property of equality
expression, may be added to both
a =equation
b, then awithout
+c = b+c
sides ofIfan
changing the solution.
Both
sides of an equation
be
The multiplication
propertymay
of equality
multiplied by the same nonzero real
a = b if and only if ac = bc and c ≠ 0
number without changing the
solution.
The properties of equality
The addition property of equality
If a = b, then a + c = b + c
The multiplication property of equality
If a = b, then ac = bc (c ≠ 0)
Solve 2 x - 8 x + 35 = 5 - 3 x .
When you are asked to solve an
equation, you always need to check
your proposed solution in the original
equation and write your answer in a
complete English sentence.
Solve 2 x - 8 x + 35 = 5 - 3 x .
Solve 7(3z - 2) + 5 = 6(2z - 1) + 24.
Solve 7(3z - 2) + 5 = 6(2z - 1) + 24.
Write an equation.
Then solve and checkit.
The sum of twice a number and 7 is
equal to the sum of the number and 6.
Find the number.
The sum of twice a number and 7 is
equal to the sum of the number and 6.
The sum of twice a number and 7 is
equal to the sum of the number and 6.
The sum of twice a number and 7 is
equal to the sum of the number and 6.
Solving equations that have fractions
If an equation contains one or more
fractions, then the solution process
is usually less taxing if you first
eliminate the fractions from the
equation.
Solving equations that have fractions
1. Determine the least common
multiple of all of the denominators
that occur in the equation.
2. Multiply both sides of the
equation by the least common
multiple found in step 1.
Solving equations that have fractions
3. Simplify both sides of the
equation. Remember to use the
distributive property on sides of
the equation that contain two or
more terms.
4. If you chose the correct LCD and
made no mistakes, then the
fractions have now been
eliminated from the equation.
Solving equations that have fractions
5. Go ahead and solve this
equivalent equation which
contains no fractions.
7
Find the solution to 3 x + 4 = .
5
7
Find the solution to 3 x + 4 = .
5
3y 2 7
Solve
- =
.
4 3 12
3y 2 7
Solve
- =
.
4 3 12
2 x x 17
Solve 2 x = +
.
7
2
2
2 x x 17
Solve 2 x = +
.
7
2
2
x
Solve
+ 13 = - 22 by clearing fractions.
2
x
Solve
+ 13 = - 22 by clearing fractions.
2
x
Solve + 13 = - 22 without clearing
2
fractions.
x
Solve + 13 = - 22 without clearing
2
fractions.
Equations in which the first step
would require fraction arithmetic if
we didn’t clear the fractions first.
3y 2 x
2 x7 17 7
Find theSolve
Solve
solution
- 3=x ++.4 = . .
2 x -to
4 73 12
2
25
Solving linear equations
1. Clear fractions by multiplying
each side of the equation by the
LCM of all of the denominators
2. Simplify each side of the
equation
3. Collect all variable terms on one
side of the equation and all
constant terms on the other side
of the equation
Solving linear equations
4. Isolate the variable and solve.
5. Check the proposed solution in
the original equation.
6. State your conclusion in a
complete English sentence.