NCERT Solutions Class 7 Maths Chapter 15 — Simple Equations

Solution:

Step 1: An equation is a mathematical statement that shows two expressions are equal, indicated by an '=' sign.

Step 2: Option A is an algebraic expression.

Step 3: Option B is an inequality because it uses '<'.

Step 4: Option D is an algebraic expression.

Step 5: Option C, 4z = 12, contains an equality sign and equates two expressions, hence it is an equation.

Solution:

Step 1: Let the unknown number be 'x'.

Step 2: 'Increased by 7' means adding 7 to the number, so it becomes x + 7.

Step 3: 'Is equal to 20' means setting the expression equal to 20.

Step 4: Combining these, the equation is x + 7 = 20.

Solution:

Step 1: Given the equation: x - 8 = 15.

Step 2: To remove -8 from the left side, we add 8 to both sides to maintain balance. [x - 8 + 8 = 15 + 8]

Step 3: Simplifying both sides gives: [x = 23]

Solution:

Step 1: The core principle of solving equations is to keep them balanced.

Step 2: This means whatever operation you perform on one side of the equation, you must perform the exact same operation on the other side.

Step 3: Therefore, adding the same number to both sides maintains the equality and keeps the equation true.

Solution:

Step 1: Given the equation: 4y = 28.

Step 2: To isolate 'y', we need to divide both sides of the equation by 4. [4y / 4 = 28 / 4]

Step 3: Simplifying both sides gives: [y = 7]