x + 3 = 7 means: "Some number plus 3 equals 7." We need to find what number x represents. In this case, x = 4 because 4 + 3 = 7.

The variable is y (it can change or vary). The constant is 8 (its value stays the same, it does not change). 3 is the coefficient (the number multiplied by the variable).

An expression (like 2x + 5) has no equals sign and represents a value. An equation (like 2x + 5 = 13) has an equals sign and shows that two expressions are equal. Equations can be solved.

Multiplication before addition: 2 × 3 = 6, then 8 + 6 = 14. Without order of operations, different people might get different answers!

Add 7 to both sides: x - 7 + 7 = 12 + 7, which simplifies to x = 19. The inverse of subtracting 7 is adding 7. Always do the same operation to both sides to keep the equation balanced.

4x means 4 times x. The inverse of multiplication is division. Divide both sides by 4: 4x ÷ 4 = 24 ÷ 4, so x = 6.

Step 1: Subtract 5 from both sides: 2x = 10. Step 2: Divide both sides by 2: x = 5. Undo addition/subtraction first, then undo multiplication/division.

Combine x terms: 3x - x = 2x. Combine y terms: 2y + 5y = 7y. So simplified expression = 2x + 7y. You cannot combine x and y terms because they are not like terms.

Multiply 3 by each term inside the parentheses: 3 × x = 3x, and 3 × 4 = 12. So 3(x + 4) = 3x + 12.

"Twice a number" = 2n. "Five less than" means subtract 5, but careful: less than reverses order. So 2n - 5, not 5 - 2n.