example
Determine whether each of the following is a solution of
x−0.7=1.5
1.
x=1
2.
x=−0.8
3.
x=2.2
Solution
1. |
|
|
x−0.7=1.5 |
Substitute 1 for x. |
1−0.7=?1.5 |
Subtract. |
0.3=1.5 |
Since
x=1 does not result in a true equation,
1 is not a solution to the equation.
2. |
|
|
x−0.7=1.5 |
Substitute 0.8 for x. |
0.8−0.7=?1.5 |
Subtract. |
−1.5=1.5 |
Since
x=−0.8 does not result in a true equation,
−0.8 is not a solution to the equation.
3. |
|
|
x−0.7=1.5 |
Substitute 2.2 for x. |
2.2−0.7=?1.5 |
Subtract. |
1.5=1.5 |
Since
x=2.2 results in a true equation,
2.2 is a solution to the equation.
example
Solve:
y+2.3=−4.7
Answer:
Solution
We will use the Subtraction Property of Equality to isolate the variable.
|
y+2.3=−4.7 |
Subtract 2.3 from each side, to undo the addition. |
y+2.3−2.3=−4.7−2.3 |
Simplify. |
y−7 |
Check: |
y+2.3=−4.7 |
|
Substitute y=−7. |
−7+2.3=?−4.7 |
|
Simplify. |
−4.7=−4.7 |
|
Since
y=−7 makes
y+2.3=−4.7 a true statement, we know we have found a solution to this equation.
example
Solve:
a−4.75=−1.39
Answer:
Solution
We will use the Addition Property of Equality.
|
a−4.75=−1.39 |
Add 4.75 to each side, to undo the subtraction. |
a−4.75+4.75=−1.39+4.75 |
Simplify. |
a=3.36 |
Check: |
a−4.75=−1.39 |
|
Substitute a=3.36. |
3.36−4.75=?−1.39 |
|
|
−1.39=−1.39 |
|
Since the result is a true statement,
a=3.36 is a solution to the equation.
example
Solve:
−4.8=0.8n
Answer:
Solution
We will use the Division Property of Equality.
Use the Properties of Equality to find a value for n.
|
−4.8=0.8n |
We must divide both sides by 0.8 to isolate n. |
0.8−4.8=0.80.8n |
Simplify. |
−6=n |
Check: |
−4.8=0.8n |
|
Substitute n=−6. |
−4.8=?0.8(−6) |
|
|
−4.8=−4.8 |
|
Since
n=−6 makes
−4.8=0.8n a true statement, we know we have a solution.
example
Solve:
−1.8p=−6.5
Answer:
Solution
We will use the Multiplication Property of Equality.
|
−1.8p=−6.5 |
Here, p is divided by −1.8. We must multiply by −1.8 to isolate p |
−1.8(−1.8p)=−1.8(−6.5) |
Multiply. |
p=11.7 |
Check: |
−1.8p=−6.5 |
|
|
−1.811.7=?−6.5 |
|
Substitute p=11.7. |
−6.5=−6.5 |
|
A solution to
−1.8p=−6.5 is
p=11.7