- Steps to solve an equation with a variable and a constant:
1. Identify the variable and the constant in the equation. The variable is usually represented by a letter like x or y. The constant is a numerical value.
2. Determine if the constant should be added or subtracted from the variable. Look for addition (+) or subtraction (-) signs in the equation.
3. Decide if the equation requires multiplication or division. Look for multiplication (x) or division (/) signs in the equation. Make sure you know if you need to multiply or divide both sides.
4. Get the variable by itself by performing the opposite mathematical operation. If the variable is added to a constant, subtract the constant from both sides. If the variable is multiplied by a constant, divide both sides by the constant.
5. Simplify the equation. Combine like terms and perform any multiplication or division needed to isolate the variable.
6. Solve for the variable. Once the variable is by itself on one side, determine its value. That value makes the original equation true.
7. Check your work by substituting the value back into the original equation. Make sure it results in a true statement.
8. Provide the solution as an answer. State the value of the variable that satisfies the equation.
For example, to solve the equation 3x + 7 = 19:
- 1. 3x is the variable. 7 is the constant.
- 2. 3x is added to 7.
- 3. 3x requires multiplication.
- 4. Subtract 7 from both sides: 3x + 7 - 7 = 19 - 7. So, 3x = 12.
- 5. No simplification needed. 3x is isolated.
- 6. Solve for x: 3x/3 = 12/3. So, x = 4.
- 7. Check: 3(4) + 7 = 19. true.
- 8. The solution is x = 4.
By plugging x = 4 in equation
- 3(4) + 7 = 19
- 12 + 7 = 19
- 19 = 19
HENCE EQUATION SATISFIED