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Algebra - Solving one-step and two-step equations

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Equation: A mathematical statement showing that two expressions are equal, separated by an '=' sign.

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Variable: A letter (like x or y) representing an unknown number that we need to find.

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Inverse Operations: Operations that undo each other. Addition is the inverse of subtraction; multiplication is the inverse of division.

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Isolating the Variable: The goal of solving an equation is to get the variable alone on one side of the equals sign.

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The Golden Rule of Algebra: Whatever operation you perform on one side of the equation, you must perform the exact same operation on the other side to keep it balanced.

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Reverse BIDMAS/BODMAS: When solving two-step equations, you generally undo addition and subtraction first, then multiplication and division.

📐Formulae

Addition/Subtraction: If x+a=bx + a = b, then x=b−ax = b - a; If x−a=bx - a = b, then x=b+ax = b + a.

Multiplication/Division: If ax=bax = b, then x=bax = \frac{b}{a}; If xa=b\frac{x}{a} = b, then x=b×ax = b \times a.

Two-Step General Form: If ax+b=cax + b = c, then ax=c−bax = c - b, and x=c−bax = \frac{c - b}{a}.

💡Examples

Problem 1:

Solve for xx: x+12=30x + 12 = 30

Solution:

x=18x = 18

Explanation:

To isolate xx, we use the inverse of adding 12, which is subtracting 12. Subtract 12 from both sides: x+12−12=30−12x + 12 - 12 = 30 - 12. This simplifies to x=18x = 18.

Problem 2:

Solve for yy: 7y=427y = 42

Solution:

y=6y = 6

Explanation:

To isolate yy, we use the inverse of multiplying by 7, which is dividing by 7. Divide both sides by 7: 7y7=427\frac{7y}{7} = \frac{42}{7}. This simplifies to y=6y = 6.

Problem 3:

Solve for zz: 3z−5=163z - 5 = 16

Solution:

z=7z = 7

Explanation:

Step 1: Use the inverse of subtracting 5. Add 5 to both sides: 3z=16+5⇒3z=213z = 16 + 5 \Rightarrow 3z = 21. Step 2: Use the inverse of multiplying by 3. Divide both sides by 3: z=213z = \frac{21}{3}. Therefore, z=7z = 7.

Problem 4:

Solve for ww: w4+2=5\frac{w}{4} + 2 = 5

Solution:

w=12w = 12

Explanation:

Step 1: Use the inverse of adding 2. Subtract 2 from both sides: w4=5−2⇒w4=3\frac{w}{4} = 5 - 2 \Rightarrow \frac{w}{4} = 3. Step 2: Use the inverse of dividing by 4. Multiply both sides by 4: w=3×4w = 3 \times 4. Therefore, w=12w = 12.