Simple (Linear) Equations (Including Word Problems)
ICSE Class 6 · Mathematics · Chapter 22
What this chapter covers
- Solving simple equations
- Word problems leading to simple equations
Key definitions
An equation is a statement that two quantities are equal, written with the equals sign = between them.
An unknown is a letter or symbol that stands for one particular number whose value you have to find.
A linear equation in one variable is an equation with only one letter, where that letter is not multiplied by itself.
The solution of an equation is the value of the unknown that makes the LHS equal to the RHS.
Transposing is moving a number from one side of an equation to the other side while changing its operation to the opposite one.
Key points
- An equation is a statement that two quantities are equal; it always has an equals sign.
- The two sides of an equation are the LHS and the RHS.
- A linear equation in one variable has one letter, which is not multiplied by itself.
- The solution, or root, is the value of the unknown that makes both sides equal.
- An equation is like a level balance: do the same thing to both sides.
- Undo the operation on the variable: subtraction undoes addition, division undoes multiplication, and the other way round.
- Transposing means moving a number to the other side and changing its operation to the opposite one: + to -, - to +, × to ÷, and ÷ to ×.
- Always check the answer by putting it back into the original equation.
- For a word problem: choose a letter, frame the equation, solve, check in the story, and answer in a sentence with units.
Questions answered
Which of these are equations: 3x + 1, 3x = 21, y - 4 = 0, 7p?
3x = 21 and y - 4 = 0 are equations, because they have an equals sign. 3x + 1 and 7p are expressions.
Name the LHS and the RHS of 2m = 18.
The LHS is 2m and the RHS is 18.
Is x = 9 the solution of x - 4 = 6?
No. Putting x = 9 gives 9 - 4 = 5, which is not 6. The solution is x = 10.
Solve z + 17 = 30.
Subtract 17 from both sides: z = 30 - 17 = 13.
Solve 8k = 72.
Divide both sides by 8: k = 72 ÷ 8 = 9.
Solve (n)/(6) = 5.
Multiply both sides by 6: n = 5 × 6 = 30.
Write an equation for: "A number decreased by 9 is 21." Then solve it.
x - 9 = 21, so x = 21 + 9 = 30. The number is 30.
A box of 6 equal packets of biscuits weighs 900 g. Find the weight of one packet, ignoring the box.
Let each packet weigh w grams. Then 6w = 900, so w = 900 ÷ 6 = 150. Each packet weighs 150 g.