Decimal equation: An equation that contains decimal numbers. To solve, isolate the variable by performing the inverse operation on both sides of the equation.
- Identify the operation being performed on the variable
- Perform the inverse operation on both sides of the equation
- Align decimal points when adding or subtracting
- Keep the variable isolated on one side
- Verify the solution by substituting back into the original equation
x = 20.7 - 12.45
x = 8.25
Since 12.45 is added to x, subtract 12.45 from both sides.
x + 12.45 - 12.45 = 20.7 - 12.45
20.70 - 12.45 = 8.25
8.25 + 12.45 = 20.7 ✓
The solution is x = 8.25
• Inverse Operation Rule: To undo addition, subtract the same number from both sides
• Decimal Alignment Rule: All decimal points must be in the same vertical column
• Equality Rule: Whatever is done to one side of the equation must be done to the other side
• Verification Rule: Always check your answer by substituting back into the original equation
Decimal equation: An equation that contains decimal numbers. To solve, isolate the variable by performing the inverse operation on both sides of the equation.
y = 15.6 + 8.34
y = 23.94
Since 8.34 is subtracted from y, add 8.34 to both sides.
y - 8.34 + 8.34 = 15.6 + 8.34
15.60 + 8.34 = 23.94
23.94 - 8.34 = 15.6 ✓
The solution is y = 23.94
• Inverse Operation Rule: To undo subtraction, add the same number to both sides
• Decimal Alignment Rule: All decimal points must be in the same vertical column
• Equality Rule: Whatever is done to one side of the equation must be done to the other side
• Verification Rule: Always check your answer by substituting back into the original equation
Decimal equation: An equation that contains decimal numbers. To solve, isolate the variable by performing the inverse operation on both sides of the equation.
24.8 - z + z = 17.35 + z
24.8 = 17.35 + z
24.8 - 17.35 = z
z = 7.45
Since z is subtracted from 24.8, add z to both sides to move it to the right side.
24.8 = 17.35 + z
24.8 - 17.35 = z
24.80 - 17.35 = 7.45
24.8 - 7.45 = 17.35 ✓
The solution is z = 7.45
• Inverse Operation Rule: To isolate a variable, perform the opposite operation
• Decimal Alignment Rule: All decimal points must be in the same vertical column
• Equality Rule: Whatever is done to one side of the equation must be done to the other side
• Verification Rule: Always check your answer by substituting back into the original equation
Definitions:
Decimal Equation: An equation that contains decimal numbers. To solve, isolate the variable by performing the inverse operation on both sides of the equation.
Inverse Operation: The opposite operation that undoes another operation. Addition and subtraction are inverse operations.
Variable: A symbol (usually a letter) that represents an unknown number.
Decimal Point: The dot that separates the whole number part from the fractional part in a decimal number.
Core Rules:
• To solve an equation, isolate the variable on one side
• Perform the same operation on both sides of the equation
• Use inverse operations to undo operations on the variable
• Always align decimal points when adding or subtracting
• Verify your solution by substituting back into the original equation
Methods and Procedures:
1. Identify the variable and the operation being performed on it
2. Perform the inverse operation on both sides of the equation
3. Align decimal points when adding or subtracting
4. Simplify both sides of the equation
5. Verify the solution by substituting back into the original equation
6. Check that both sides of the equation are equal
Examples:
Simple: x + 12.45 = 20.7 → x = 20.7 - 12.45 = 8.25
Subtraction: y - 8.34 = 15.6 → y = 15.6 + 8.34 = 23.94
Complex: 24.8 - z = 17.35 → z = 24.8 - 17.35 = 7.45
Tips and Tricks:
• Always align decimal points when adding or subtracting
• Add placeholder zeros to make decimal places match
• Check your answer by substituting it back into the original equation
• Remember: addition and subtraction are inverse operations
• Use graph paper to help keep numbers aligned
Key Notes to Remember:
• Whatever you do to one side of the equation, you must do to the other side
• The goal is to get the variable by itself on one side
• Verification is crucial - it confirms your solution is correct
• Misaligned decimal points lead to incorrect answers
Then x = b - a
If x - a = b
Then x = b + a
Decimal Equation: An equation that contains decimal numbers
Inverse Operation: The opposite operation that undoes another operation
Variable: A symbol that represents an unknown number
Decimal Point: The dot that separates the whole number part from the fractional part
- Identify variable: Locate the unknown in the equation
- Determine operation: Identify what operation is being performed on the variable
- Apply inverse: Perform the opposite operation on both sides
- Align decimals: Ensure decimal points are properly aligned when adding/subtracting
- Simplify: Calculate both sides of the equation
- Verify: Substitute the solution back into the original equation
• Isolate variable: Get the variable by itself on one side of the equation
• Inverse operations: To undo addition, subtract; to undo subtraction, add
• Both sides: Whatever you do to one side, you must do to the other side
• Decimal alignment: Always align decimal points when adding or subtracting
• Verification: Always check your solution by substituting back into the original equation
Decimal equation: An equation that contains decimal numbers. To solve, isolate the variable by performing the inverse operation on both sides of the equation.
w = 32.7 - 18.25
w = 14.45
Since 18.25 is added to w, subtract 18.25 from both sides.
w + 18.25 - 18.25 = 32.7 - 18.25
32.70 - 18.25 = 14.45
14.45 + 18.25 = 32.7 ✓
The solution is w = 14.45
• Inverse Operation Rule: To undo addition, subtract the same number from both sides
• Decimal Alignment Rule: All decimal points must be in the same vertical column
• Equality Rule: Whatever is done to one side of the equation must be done to the other side
• Verification Rule: Always check your answer by substituting back into the original equation
Decimal equation: An equation that contains decimal numbers. To solve, isolate the variable by performing the inverse operation on both sides of the equation.
45.6 - t + t = 28.95 + t
45.6 = 28.95 + t
45.6 - 28.95 = t
t = 16.65
Since t is subtracted from 45.6, add t to both sides to move it to the right side.
45.6 = 28.95 + t
45.6 - 28.95 = t
45.60 - 28.95 = 16.65
45.6 - 16.65 = 28.95 ✓
The solution is t = 16.65
• Inverse Operation Rule: To isolate a variable, perform the opposite operation
• Decimal Alignment Rule: All decimal points must be in the same vertical column
• Equality Rule: Whatever is done to one side of the equation must be done to the other side
• Verification Rule: Always check your answer by substituting back into the original equation