Transcript simple equations

Equations
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Equations
Using inverse operations
Solving equations by transforming both sides
Solving an equation with unknowns on both sides
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Equations
An equation links an algebraic expression and a number,
or two algebraic expressions with an equals sign.
For example:
x + 7 = 13 is an equation.
In an equation the unknown usually has a particular value.
Finding the value of the unknown is called solving the
equation.
x + 7 = 13
x=6
When we solve an equation we always line up the equals signs.
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Using inverse operations
In algebra, letter symbols represent numbers.
Rules that apply to numbers in arithmetic
apply to letter symbols in algebra.
In arithmetic, if 3 + 7 = 10, we can
use inverse operations to write:
10 – 7 = 3
and
10 – 3 = 7
In algebra, if a + b = 10, we can use inverse operations
to write:
or
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10 – b = a
and
10 – a = b
a = 10 – b
and
b = 10 – a
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Using inverse operations
In arithmetic, if 3 × 4 = 12, we can use inverse operations
to write:
12 ÷ 4 = 3
and
12 ÷ 3 = 4
In algebra, if ab = 12, we can use inverse operations to
write:
12 = a
b
or
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a = 12
b
and
12 = b
a
and
b = 12
a
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Using inverse operations to solve equations
We can use inverse operations to solve simple equations.
For example:
x + 5 = 13
x = 13 – 5
x=8
Always check the solution to an equation by substituting
the solution back into the original equation.
If we substitute x = 8 back into x + 5 = 13 we have
8 + 5 = 13
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Using inverse operations to solve equations
Solve the following equations using inverse operations.
17 – x = 6
5x = 45
x = 45 ÷ 5
17 = 6 + x
17 – 6 = x
x=9
11 = x
Check:
5 × 9 = 45
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x = 11
We always write
the letter before
the equals sign.
Check:
17 – 11 = 6
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Using inverse operations to solve equations
Solve the following equations using inverse operations.
x
7
=3
x=3×7
x = 21
Check:
21
7
=3
3x – 4 = 14
3x = 14 + 4
3x = 18
x = 18 ÷ 3
x=6
Check:
3 × 6 – 4 = 14
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Solving equations by transforming both sides
Solve this equation by transforming both sides in the same
way:
m
–1=2
4
+1 +1
Add 1 to both sides.
m
=3
4
×4 ×4
Multiply both sides by 4.
m = 12
We can check the solution by substituting it back into the
original equation:
12 ÷ 4 – 1 = 2
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Solving an equation with unknowns on both sides
Let’s solve this equation by transforming both sides of the
equation in the same way.
3n – 11 = 2n – 3
Start by writing the equation down.
−2n
Subtract 2n from both sides.
−2n
n – 11 = –3
+11
+11
n = 8
Always line up the equals signs.
Add 11 to both sides.
This is the solution.
We can check the solution by substituting it back into the
original equation:
3  8 – 11 = 2  8 – 3
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