How do you solve equations using addition and subtraction in mathematics?
Solving equations using addition and subtraction is one of the fundamental techniques in algebra. These methods help to isolate the variable of interest on one side of the equation, making it easier to solve for that variable. Let’s explore this step-by-step.
1. Understand the Problem:Start by carefully reading the equation. Identify the variable (usually represented by a letter like x, y, or z) that you need to solve for.
Example:Consider the equation:x - 4 = 8
2. Isolate the Variable:To solve for the variable, you need to isolate it on one side of the equation. This means you need to get x alone.
For the given example, the equation is x - 4 = 8. Here, x is being subtracted by 4. The goal is to get rid of the -4 from the left side to have only x.
3. Use Addition or Subtraction:To cancel out a number, use the opposite operation. In this example, x is being subtracted by 4. The opposite of subtraction is addition. Therefore, add 4 to both sides of the equation.
Example:x - 4 + 4 = 8 + 4
When you simplify both sides, you get:x = 12
4. Verify the Solution:Always substitute the value back into the original equation to ensure it satisfies the equation.
Example:Originally, x - 4 = 8
Substitute x with 12:12 - 4 = 8
Since both sides equal, the solution x = 12 is correct.
Example with Addition:Suppose the equation is:y + 5 = 9
Steps:1. Identify the variable and the operations involved.2. Since y is being added to 5, we will subtract 5 from both sides to isolate y.
y + 5 - 5 = 9 - 5
Simplifying both sides gives:y = 4
Verification:Substitute y back into the original equation:4 + 5 = 9
The equation is satisfied, confirming that y = 4 is correct.
5. Equations with Multiple Operations:If an equation involves both addition and subtraction, you can still apply these principles step-by-step to isolate the variable.
Example:z - 3 + 7 = 10
Steps:- You can combine like terms on the left-hand side first:z - 3 + 7 simplifies to z + 4
So, the equation becomes:z + 4 = 10
- Next, subtract 4 from both sides:z + 4 - 4 = 10 - 4
This simplifies to:z = 6
Verification:Substitute z back into the original equation:6 - 3 + 7 = 103 + 7 = 1010 = 10
Since both sides of the equation are equal, z = 6 is correct.
Summary:
- Identify the variable to solve for.- Use addition to cancel out subtraction and vice versa to isolate the variable.- Simplify both sides of the equation.- Always verify your solution by substituting the variable back into the original equation.
These steps ensure a systematic approach to solving equations using addition and subtraction. Happy problem-solving!
Solve each system. To do so, substitute a for $\frac{1}{x}$ and $b$ for $\frac{1}{y}$ and solve for a and $b$. Then find $x$ and $y$ using the fact t…
A soap film $(n=1.33)$ is contained within a rectangular wire frame. The frame is held vertically so that the film drains downward and forms a wedge …
A linear function that models tuition and fees at public four year colleges from 2000 through 2016 has negative slope.
The structure of vitamin $\mathrm{C},$ whose chemical name is ascorbic acid, is drawn below (without lone pairs of electrons). (FIGURE CANNOT COPY)…
Watch the video solution with this free unlock.
EMAIL
PASSWORD