What is the process for solving one-step equations using addition and subtraction?
To solve a one-step equation using addition and subtraction, follow these steps:
1. Identify the variable: Look for the letter or symbol that represents the unknown quantity in the equation. For example, in the equation, 3x + 5 = 20, the variable is 'x.'
2. Isolate the variable: Use inverse operations to move all other terms away from the variable. If there are addition or subtraction terms on the same side as the variable, you need to perform the opposite operation to move them to the other side of the equation.
- If there is an addition term, perform subtraction, and vice versa. For example, if you have 3x + 5 = 20, subtract 5 from both sides: 3x = 20 - 5, which simplifies to 3x = 15.
- If there are multiple terms, repeat this process until you have only the variable on one side of the equation.
3. Solve for the variable: If the variable is still multiplied by a coefficient or further simplified, perform the inverse operation to isolate the variable completely.
- If the variable is multiplied by a coefficient, divide both sides of the equation by that coefficient. For example, if you have 3x = 15, divide both sides by 3: (3x)/3 = 15/3, which simplifies to x = 5.
- If the variable is divided, multiply both sides of the equation by the numerator of the fraction. For example, if you have (1/2)x = 3, multiply both sides by 2: 2 * (1/2)x = 2 * 3, simplifying to x = 6.
4. Check your solution: Substitute the value you found for the variable back into the original equation and verify if it satisfies the equation. If it does, then your solution is correct. If not, re-check your work.
Remember, the key is to perform the same operation on both sides of the equation to keep it balanced.