NCERT Solutions Class 8 Maths Chapter 10 — Linear Equations

Solution:

Step 1: A linear equation in one variable is an equation where the highest power of the variable is 1.

Step 2: In options A, B, and C, the variables x, y, and z all have a power of 1.

Step 3: In option D, the variable 'p' has a power of 2 (p²), making it a quadratic equation, not a linear equation.

Solution:

Step 1: When a term is transposed from one side of the equation to the other, its sign changes.

Step 2: Ravi correctly transposed 2x from the right side to the left side (2x became -2x).

Step 3: However, when transposing +3 from the left side to the right side, it should become -3, not +3.

Step 4: The correct first step after transposing would be 5x - 2x = -6 - 3.

Solution:

Step 1: Let the number be 'x'.

Step 2: Five times the number with 7 added: 5x + 7.

Step 3: Three times the number with 10 added: 3x + 10.

Step 4: Set them equal: 5x + 7 = 3x + 10.

Step 5: Solve for x: 5x - 3x = 10 - 7 => 2x = 3 => x = 3/2.

Solution:

Step 1: Option A is false: Adding a number to only one side changes the equality.

Step 2: Option B is false: Multiplying both sides by zero makes both sides zero, which changes the original equation and its solution (e.g., 2x=4 becomes 0=0).

Step 3: Option C is true: This is a fundamental property of equality, allowing us to simplify equations. The number must be non-zero to avoid division by zero.

Step 4: Option D is false: To maintain equality, the *same* number must be subtracted from both sides.

Solution:

Step 1: Expand the bracket: 3x - 6 + 5 = 2x - 1.

Step 2: Combine constants on the left side: 3x - 1 = 2x - 1.

Step 3: Transpose terms: 3x - 2x = -1 + 1.

Step 4: Simplify: x = 0.