Page 4
Solving for x by Adding the same number to
both sides of an equation
The Addition Property of Equality states that
you can add the same number to both sides of an equation
and still have an equivalent equation
Using the Addition Property to Solve for x.
If a constant has been subtracted from the variable term you add that constant to both sides
of the equation. The number being added to both sides of the equation is written under both sides
of the original equation.
Example 1
Solve: x − 3 = 10
Example 2
Solve: − 7 = x − 4
Example 3
Solve: − 6 = x − 6
3 has been subtracted from x
to undo this you
add 3 to both sides
of x − 3 = 10
4 has been subtracted from x
to undo this you
add 4 to both sides
of − 7 = x − 4
6 has been subtracted from x
to undo this
you add 6 to both sides
of − 6 = x − 6
x − 3 = 10
+ 3 +3
to get the solution
x = 13
−7= x−4
+4
+4
to get the solution
−3 = x
− 6 = x −6
+6 +6
to get the solution
0= x
Check: 13 − 3 = 10
Check: − 7 = −3 − 4
Check: − 6 = 0 − 6
Solve for x using the Addition Property of Equality
1. x − 11= 2
7 – 4 Answers
1. x = 13
2. x = 16
Chapter 7
2.
x − 6 = 10
3. −3 = x
3. −8 = x − 5
4. −7 = x − 2
4. −5 = x
© 2015 Eitel
Page 5
Solving for x by Subtracting the same number from
both sides of an equation
The Subtraction Property of Equality states that
you can subtract the same number from both sides of an equation
and still have an equivalent equation
Using the Subtraction Property to Solve for x.
If a constant has been added to the variable term then you subtract that constant from both
sides of the equation. The number being subtracted from both sides of the equation is written under
both sides of the original equation
Example 1
Solve: x + 2 = 6
Example 2
Solve: 4 = x + 9
2 has been added to x
to undo this you
subtract 2 from both sides
of x + 2 = 6
9 has been added to x
to undo this you
subtract 9 from both sides
of 4 = x + 9
Example 3
Solve: 1 = x + 8
8 has been added to x
to undo this you
subtract 8 from both sides
of 1 = x + 8
x+2 = 6
−2 − 2
to get the solution
x =4
4 = x+9
−9 − 9
to get the solution
−5 = x
1= x + 8
−8 − 8
to get the solution
−7 = x
Check: 4 + 2 = 6
Check: 4 = −5 + 9
Check: 1 = −7 + 8
Solve for x using the Subtraction Property of Equality.
1. x + 4 = 9
7 – 5 Answers
1. x = 5
2. x = −11
Chapter 7
2.
x + 8 = −3
3. 8 = x
3. 10 = x + 2
4. 5 = x + 5
4. 0 = x
© 2015 Eitel
Page 6
Solving for x
by dividing both sides of an equation by the same number
The Division Property of Equality states that
you can divide both sides of an equation by the same number
and still have an equivalent equation
Using the Division Property to Solve for x.
If the variable has been multiplied by a coefficient then you divide both sides of the equation
by the coefficient. Draw a division bar under both sides of the original equation and divide both
sides of the equation by the coefficient.
Example 1
Solve: 5x = 15
Example 2
Solve: 30 = −6x
Example 3
Solve: − x = −8
x has been multiplied by 5
to undo this you
divide both sides
of 5x = 15 by 5
x has been multiplied by − 6
to undo this you
divide both sides
of 30 = −6x by 6
x has been multiplied by −1
to undo this you
divide both sides
of − x = −8 by −1
5x 15
=
5
5
to get the solution
x=3
30 −6x
=
−6 −6
to get the solution
−5 = x
−1x −8
=
−1 −1
to get the solution
x=8
Check: 5(3) = 15
Check: 30 = −6(−5)
Check: − (8) = −8
Solve for x using the Division Property of Equality.
1. 5x = 20
7 – 6 Answers
1. x = 4
2. x = −11
Chapter 7
2.
−3x = 33
3. −5 = x
3. 30 = −6 x
4. −4 = −x
4. 4 = x
© 2015 Eitel
Page 7
Solving for x
by multiplying both sides of an equation by the same number
The Multiplication Property of Equality states that
you can multiply both sides of an equation by the same number
and still have an equivalent equation
Using the Multiplication Property to Solve for x.
If the variable has been divided by a number then you multiply both sides of the equation by that
number. Parenthesis ( ) must be used to show the multiplication on both sides of the equation
by the divisor.
Example 1
x
Solve:
= 3
2
Example 2
x
Solve 5 =
−3
Example 3
x
Solve:
= −1
−4
x has been divided by 2
to undo this you
multiply both sides
x
of
= 3 by 2
2
x has been divided by − 3
to undo this you
multiply both sides
x
of 5 =
by − 3
−3
x has been divided by − 4
to undo this you
multiply both sides
x
of
= −1 by − 4
−4
x
= 3(2)
2
to get the solution
x=6
x
(−3)
−3
to get the solution
−15 = x
x
= −1(−4)
−4
to get the solution
x =4
(−3)5 =
(2)
Check:
6
= 3
2
Check: 5 =
(−4)
−15
−3
Check:
4
= −1
−4
Solve for x using the Multiplication Property of Equality
1.
x
=4
5
7 – 7 Answers
1. x = 20
2. x = 18
Chapter 7
2.
x
=−6
−3
3. −10 = x
3.
5=
x
−2
4.
−3 =
x
−4
4. 12 = x
© 2015 Eitel