Grade 8 Equations in One Variable

Step 1: An **equation** is a mathematical statement that shows that two expressions are equal. It always contains an equals sign (=).

Step 2: It has a **Left Hand Side (LHS)** and a **Right Hand Side (RHS)**, separated by the equals sign.
Example: In x + 5 = 12, x + 5 is the LHS and 12 is the RHS.

Step 3: An equation often contains a **variable**, which is a symbol (usually a letter like x, y, or a) that represents an unknown value.

Step 4: A **constant** is a value that does not change (like the numbers 5 and 12 in the example).

Step 5: Solving an equation means finding the value(s) of the variable that make the equation true. This value is called the **solution**.

Step 1: The goal is to isolate the variable (x) on one side of the equation. Think of the equation as a balance scale. Whatever you do to one side, you must do to the other to keep it balanced.

Step 2: To get x by itself on the LHS, we need to remove the +7. The opposite of adding 7 is subtracting 7.

Step 3: Subtract 7 from **both** sides of the equation to maintain the balance.
x + 7 - 7 = 15 - 7

Step 4: Simplify both sides.
x + 0 = 8
x = 8

Step 5: The solution is x = 8. You can check this by substituting 8 back into the original equation: 8 + 7 = 15, which is true.

Step 1: The equation 4y = 28 means 4 times y equals 28. To isolate y, we need to undo the multiplication by 4.

Step 2: The opposite of multiplying by 4 is dividing by 4.

Step 3: Divide **both** sides of the equation by 4 to maintain the balance.
4y / 4 = 28 / 4

Step 4: Simplify both sides.
y = 7

Step 5: The solution is y = 7. Check: 4 * 7 = 28, which is true.

Step 1: The transposition method involves moving terms from one side of the equation to the other. When a term moves to the other side, its operation changes to the opposite operation (addition becomes subtraction, multiplication becomes division, etc.).

Step 2: Move the constant term (-3) from the LHS to the RHS. When -3 moves, it becomes +3.
2m = 9 + 3

Step 3: Simplify the RHS.
2m = 12

Step 4: Now, isolate m. The term 2m means 2 times m. Move the 2 from the LHS to the RHS. When 2 moves, the multiplication becomes division.
m = 12 / 2

Step 5: Perform the division.
m = 6

Step 6: The solution is m = 6. Check: 2(6) - 3 = 12 - 3 = 9, which is true.