Solving equations by adding and subtracting
Why did the math book go to the circus?
Because it needed help from a clown to solve all those equations!
But in all seriousness, adding and subtracting are basic operations that can be used to solve equations. Let's go step by step:
1. Start by isolating the variable term on one side of the equation.
For example, let's solve the equation: 2x + 5 = 11
To isolate the variable term 2x, we can subtract 5 from both sides of the equation:
2x + 5 - 5 = 11 - 5
2x = 6
2. Next, divide both sides of the equation by the coefficient of the variable to find the value of x.
In this case, the coefficient of x is 2, so we divide both sides by 2:
2x/2 = 6/2
x = 3
So, the solution to the equation is x = 3.
Remember, adding and subtracting can help you isolate the variable term and simplify the equation to find the solution!
Solving equations by adding and subtracting is one of the fundamental methods used in algebra. It allows us to manipulate equations in order to isolate a variable and find its value. Here's how you can solve equations by adding and subtracting:
1. Start by simplifying the equation as much as possible. This may involve combining like terms or distributing any constants if necessary.
2. Identify the variable (usually represented by a letter) that you want to solve for. The goal is to isolate this variable on one side of the equation.
3. Start by adding or subtracting the same value to both sides of the equation. The value you choose should help eliminate any terms that contain the variable you are trying to isolate.
4. Continue performing addition or subtraction until you have isolated the variable on one side of the equation and all other terms on the other side.
5. Once you have isolated the variable, simplify the equation further if needed. This may involve combining like terms or performing any necessary operations (e.g., division or multiplication).
6. Finally, check your solution by substituting the value you obtained for the variable back into the original equation. If both sides of the equation are equal when the variable is replaced with its value, then your solution is correct.
Here's an example to illustrate how to solve an equation using addition and subtraction:
Example: Solve the equation 3x + 7 = 22
1. Begin by simplifying the equation. No further simplification is needed in this case.
2. Identify the variable you want to solve for, which is x in this case.
3. Start by subtracting 7 from both sides of the equation to get 3x = 15.
4. Divide both sides of the equation by 3 to isolate the variable, which gives x = 5.
5. The solution is x = 5.
6. To check if the solution is correct, substitute x = 5 back into the original equation: 3(5) + 7 = 15 + 7 = 22. Both sides of the equation are equal, so the solution is correct.
By following these steps, you can solve equations by adding and subtracting. This method is a fundamental technique in algebra and can be used to solve a wide range of mathematical problems.
Solving equations by adding and subtracting involves isolating the variable by performing addition or subtraction operations on both sides of the equation. Here are the steps to solve an equation using these operations:
Step 1: Identify the equation you need to solve.
Step 2: Simplify both sides of the equation if necessary by combining like terms.
Step 3: Determine which variable you want to isolate. This is usually the variable you want to solve for.
Step 4: Add or subtract the same value to both sides of the equation to eliminate terms and isolate the variable.
Step 5: Repeat step 4 if needed until the variable is isolated on one side of the equation and constants are on the other side.
Step 6: Simplify both sides if necessary and perform any further operations.
Step 7: Check your answer by substituting the calculated value back into the original equation to ensure it is correct.
Let's go through an example to demonstrate these steps:
Example: Solve the equation 4x - 2 = 10.
Step 1: Identify the equation you need to solve: 4x - 2 = 10.
Step 2: Simplify both sides if necessary: No simplification needed in this example.
Step 3: Determine which variable to isolate: We want to solve for "x".
Step 4: Add 2 to both sides to eliminate the constant term on the left side: 4x - 2 + 2 = 10 + 2.
Simplified equation: 4x = 12.
Step 5: The variable is already isolated. We don't need to perform any additional addition or subtraction.
Step 6: Simplify both sides if necessary: No further simplification needed in this example.
Step 7: Check the answer by substituting it back into the original equation: 4(3) - 2 = 10. If both sides of the equation are equal, then the solution is correct.
In this case, 12 - 2 equals 10, so the solution is confirmed.
Thus, the solution to the equation 4x - 2 = 10 is x = 3.