Algebra
Grade 3-5Linear Equations
Solving a linear equation means finding the value of the unknown letter that makes the equation true, always by doing the same operation to both sides to keep it balanced. This lesson covers solving one-step and two-step equations, solving equations with the unknown on both sides, and solving equations that include brackets.
What you need to know
- Do the same operation to both sides to keep the equation balanced.
- Undo operations in reverse order: deal with plus and minus before times and divide.
- For letters on both sides, collect the letters on one side and the numbers on the other.
- Check your answer by substituting it back into the original equation.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Solving a one-step equation
Do the inverse operation to both sides of the equation to leave the letter on its own.
To solve x + 7 = 12, subtract 7 from both sides: x = 12 − 7 = 5.
Solving a two-step equation
Undo addition or subtraction first, then undo multiplication or division, always doing the same thing to both sides.
To solve 3x + 5 = 20, subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5.
Solving equations with the unknown on both sides
Move all the letter terms to one side and all the number terms to the other, by adding or subtracting the same term from both sides, then solve as usual.
To solve 5x + 3 = 2x + 18, subtract 2x from both sides to get 3x + 3 = 18, then subtract 3 to get 3x = 15, giving x = 5.
Solving equations with brackets
Expand the bracket first, then solve the resulting equation as usual.
To solve 3(x + 2) = 21, expand the bracket to get 3x + 6 = 21, then subtract 6 to get 3x = 15, giving x = 5.
Worked examples
Three exam-style questions, fully solved
Solve x + 7 = 12.
Easy- 1.Subtract 7 from both sides: x = 12 − 7
Answer: x = 5
Solve 5x + 3 = 2x + 18.
Medium- 1.Subtract 2x from both sides: 3x + 3 = 18
- 2.Subtract 3 from both sides: 3x = 15
- 3.Divide both sides by 3: x = 5
Answer: x = 5
Solve 3(x + 2) = 21.
Hard- 1.Expand the bracket: 3x + 6 = 21
- 2.Subtract 6 from both sides: 3x = 15
- 3.Divide both sides by 3: x = 5
Answer: x = 5
Practice
6 questions, marked instantly
Type an answer and check it. The worked solution appears once you have had a go. No login needed, and your progress saves in this browser.
Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
Solve 3x = 21.
Solve x + 9 = 4.
Solve 2x + 5 = 17.
Solve 4x − 3 = 2x + 7.
Solve 3(x − 2) = 18.
Solve 5(x + 2) = 3(x + 6).
Avoid these
The mistakes students make most often
Doing an operation to only one side of the equation, instead of applying it to both sides to keep the equation balanced.
Getting the sign wrong when moving a term across the equals sign, forgetting that a term being added becomes subtracted (and vice versa) once it moves.
When the unknown appears on both sides, subtracting the larger x-term first, which leads to unnecessary negative numbers instead of collecting onto the side with the larger coefficient.
Forgetting to expand a bracket before starting to solve an equation that includes one.
Not checking the solution by substituting it back into the original equation to confirm both sides give the same value.
FAQ
Questions students and parents ask
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What to learn next
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