Solving Simple, Multi-Step Equations And Equations With Variables On Both Sides Worksheet Page 21
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40Lesson
1.3
Lesson Tutorials
Solving Equations with Variables on Both Sides
To solve equations with variables on both sides, collect the variable
terms on one side and the constant terms on the other side.
Solving an Equation with Variables on Both Sides
1 1
EXAMPLE
Solve 15 − 2x = −7x. Check your solution.
15 − 2x = −7x
Write the equation.
+ 2x
+ 2x
Undo the subtraction.
Addition Property of Equality
15 = −5x
Simplify.
Check
−5x
15
Division Property
=
—
—
Undo the multiplication.
15 −
=
−7x
2x
−5
−5
of Equality
?
−3 = x
15 −
=
−7(−3)
Simplify.
2(−3)
✓
21 = 21
The solution is x = −3.
2 2
Using the Distributive Property to Solve an Equation
EXAMPLE
(
)
1
Solve −2(x − 5) = 6
2 −
—
x
.
2
(
)
1
−2(x − 5) =
2 −
6
—
x
Write the equation.
2
−2x + 10 =
12 − 3x
Distributive Property
+ 3x
+ 3x
Undo the subtraction.
Addition Property of Equality
x + 10 =
12
Simplify.
− 10
− 10
Undo the addition.
Subtraction Property of Equality
x = 2
Simplify.
The solution is x = 2.
Solve the equation. Check your solution.
1. −3x = 2x + 19
2. 2.5y + 6 = 4.5y − 1
3. 6(4 − z) = 2z
Exercises 6 –14
20
Chapter 1
Equations
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