Solving Equations
Solving equations means finding the value of x that makes the equation true. To solve 3x + 2 = 11, subtract 2 from both sides to get 3x = 9, then divide both sides by 3, so x = 3.
Video Lesson
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Flashcards
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Solving an Equation
- Solving an equation means finding the value of x that makes the equation true.
- You can check the solution by substituting the value of x and seeing if both sides are equal.
Simplify Both Sides
- Use the distributive law to expand brackets.
- Collect like terms to simplify each side of the equation.
Rearrange and Solve
- Move all terms with x to one side and all constants to the other side.
- Divide by the coefficient of x to find the value of x.
Practice Questions
Test your understanding
Solve the equation: .
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The has had 4 subtracted from it, so add 4 to both sides: .
The is multiplied by 2, so divide both sides by 2: .
Check: . Correct.
Solve the equation: .
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The has had 2 added to it, so subtract 2 from both sides: .
The is multiplied by 3, so divide both sides by 3: .
Check: . Correct.
Solve the equation: .
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Expand the bracket, multiplying both terms inside by 2: .
Subtract 8 from both sides: . Divide both sides by 2: .
(You could also divide both sides by 2 first: , which again gives .)
Check: . Correct.
Solve the equation: .
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Get the terms on one side by subtracting from both sides: .
Subtract 3 from both sides: . Divide both sides by 2: .
Check: and . Both sides match, so .
Solve the equation: .
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Expand the left side, multiplying both terms inside the bracket by 3: .
Subtract from both sides: . Add 6 to both sides: .
Check: and . Both sides match, so .
Simplify the expression: .
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Expand each product, multiplying every term inside the bracket by the term outside.
and .
Now collect like terms: , and .
An term and an term are not like terms, so they cannot be combined any further. The simplified expression is .
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Interactive Activity
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Solving Equations frequently asked questions
The questions students bump into most on this topic
Substitute your value back into the original equation and work out each side. If the left side equals the right side, your solution is correct. For example, in x + 3 = 8, the value x = 5 gives 5 + 3 = 8. That is true, so x = 5 is correct.
Expand the brackets first using the distributive law, multiplying the term outside by each term inside. Then collect like terms to simplify each side. After that, rearrange the equation to gather unknowns on one side and constants on the other. Finally, divide by the coefficient of the unknown.
Bring all the unknowns to one side by subtracting the smaller unknown term from both sides. This leaves the unknowns on one side and the constants on the other. Then subtract any constant to isolate the unknown, and divide both sides by its coefficient to find the value.
Doing the same operation to both sides keeps the equation balanced, so both sides stay equal. The solution does not change, because the value of the unknown still makes the equation true. If you changed only one side, the two sides would no longer match and your answer would be wrong.
First, simplify both sides of the equation. Expand any brackets using the distributive law, then collect like terms so each side is as simple as possible. Once both sides are simplified, rearrange to bring unknowns and constants to opposite sides. Then solve for the unknown.