Solving Equations

Q: How do you check the solution to an equation?

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.

Q: How do you solve equations with brackets?

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.

Q: Why do you do the same operation to both sides of an equation?

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.

Q: What do you do first when solving an equation?

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.

Key concept

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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$Solving Equations poster$

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Flashcards

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Solving an equation means finding the value of the unknown that makes the equation true, shown with the example x + 3 = 8, where x = 5.

Solving a linear equation using distributive law and simplification, steps: simplify both sides, rearrange the equation, and solve for the unknown.

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.

Practice Questions

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Solve the equation: $2 x - 4 = 6$ .

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Interactive Activity

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Students Also Ask

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How do you check the solution to an equation?

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.

How do you solve equations with brackets?

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.

How do you solve equations with unknowns on both sides?

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.

Why do you do the same operation to both sides of an equation?

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.

What do you do first when solving an equation?

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.

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