example
Write an equation modeled by the envelopes and counters, and then solve the equation:

Solution
On the left, write x for the contents of the envelope, add the 4 counters, so we have x+4 . |
x+4 |
On the right, there are 5 counters. |
5 |
The two sides are equal. |
x+4=5 |
Solve the equation by subtracting 4 counters from each side. |
|

We can see that there is one counter in the envelope. This can be shown algebraically as:
x+4=5
x+4−−4=5−−4
x=1
Substitute
1 for
x in the equation to check.
x+4=5
1+4=5
5=5
Since
x=1 makes the statement true, we know that
1 is indeed a solution.
try it
Write the equation modeled by the envelopes and counters, and then solve the equation:
x+1=7[/latex][latex]x=6
Write the equation modeled by the envelopes and counters, and then solve the equation:
x+3=4[/latex] [latex]x=1
example
Solve:
x+8=17.
Answer:
Solution
We will use the Subtraction Property of Equality to isolate x.
|
x+8=17 |
Subtract 8 from both sides. |
x+8−−8=17−−8 |
Simplify. |
x=9 |
|
x+8=17 |
|
9+8=17 |
|
17=17 |
Since
x=9 makes
x+8=17 a true statement, we know
9 is the solution to the equation.
example
Solve:
100=y+74.
Answer:
Solution
To solve an equation, we must always isolate the variable—it doesn’t matter which side it is on. To isolate y, we will subtract 74 from both sides.
|
100=y+74 |
Subtract 74 from both sides. |
100−−74=y+74−−74 |
Simplify. |
26=y |
Substitute 26 for y to check.
100=y+74
100=26+74
100=100 |
|
Since
y=26 makes
100=y+74 a true statement, we have found the solution to this equation.
example
Solve:
x−5=8.
Solution
We will use the Addition Property of Equality to isolate the variable.
|
x−−5=8 |
Add 5 to both sides. |
x−−5+5=8+5 |
Simplify. |
x=13 |
Now we can check. Let x=13. |
|
x−−5=8 |
|
13−−5=8 |
|
8=8 |
|
example
Solve:
27=a−16.
Answer:
Solution
We will add 16 to each side to isolate the variable.
|
27=a−−16 |
Add 16 to each side. |
27+16=a−−16+16 |
Simplify. |
43=a |
Now we can check. Let a=43. |
27=a−−16 |
|
27=43−−16 |
|
27=27 |
The solution to
27=a−16 is
a=43.