Solving Simple, Multi-Step Equations And Equations With Variables On Both Sides Worksheet Page 22
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40Some equations do not have one solution. Equations can also have no
solution or infi nitely many solutions.
When solving an equation that has no solution, you will obtain an
equivalent equation that is not true for any value of the variable, such
as 0 = 2.
Solving Equations with No Solution
3 3
EXAMPLE
Solve 3 − 4x = −7 − 4x.
3 − 4x = −7 − 4x
Write the equation.
+ 4x
+ 4x
Addition Property of Equality
Undo the subtraction.
✗
3 = − 7
Simplify.
The equation 3 = −7 is never true. So, the equation has
no solution.
When solving an equation that has infi nitely many solutions, you
will obtain an equivalent equation that is true for all values of the variable,
such as − 5 = − 5.
4 4
Solving Equations with Infi nitely Many Solutions
EXAMPLE
(
)
3
Solve 6x + 4 = 4
x + 1
—
.
2
(
)
3
6x + 4 = 4
x + 1
—
Write the equation.
2
6x + 4 = 6x + 4
Distributive Property
− 6x
− 6x
Subtraction Property of Equality
Undo the addition.
4 = 4
Simplify.
The equation 4 = 4 is always true. So, the equation has infi nitely
many solutions.
Solve the equation.
Exercises 18 –29
1
4. 2x + 1 = 2x − 1
(6t − 4) = 3t − 2
—
5.
2
(
)
2
9
1
(2b + 9) =
b +
7. 6(5 − 2v) = −4(3v + 1)
—
—
—
6.
3
2
3
Section 1.3
Solving Equations with Variables on Both Sides
21
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