Solving Linear Equations

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Questions and Answers

Your friend solves the equation -3(x+6)= 12. Is your friend correct? ______

What does x equal in the equation -3x = 6? x = ______

-2

Fill in the blank: i ➡ Listen YOU BE THE ______

TEACHER

Fill in the blank: B = Explain your ______.

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Fill in the blank: Save / Exit ______.

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Flashcards

Solving an equation

An equation is a statement that two expressions are equal. To solve an equation, you need to find the value of the variable that makes the equation true. In this case, the value of x that satisfies the equation -3x = 6 is -2.

Distributing in an equation

When simplifying an algebraic expression, we first need to distribute the number outside the parenthesis to each term inside. Then, we combine like terms. In this case, we distribute -3 to both x and 6 to get -3x -18 = 12.

Isolating the variable

In general, an equation can be solved by isolating the variable. The process involves moving all terms containing the variable to one side of the equation and all constants to the other side.

Variable in an equation

A variable is a symbol that represents an unknown value. In most cases, we use letters like x or y as variables. In the equation -3x = 6, the variable x represents the unknown value we need to find.

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Checking the solution

To check if a solution is correct, we substitute the solution back into the original equation. If the equation holds true, then the solution is correct. For example, plugging -2 for x in -3x = 6 results in 6 = 6, confirming that -2 is the correct solution.

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Study Notes

Solving the Equation -3(x+6) = 12

The equation -3(x+6) = 12 is solved by multiplying the terms inside the parentheses by -3, resulting in -3x - 18 = 12.
The next step is to add 18 to both sides of the equation, resulting in -3x = 30.
Finally, dividing both sides of the equation by -3 results in x = -10.
The friend's solution, x = -2, is incorrect.

Friend's Mistakes

The friend multiplied both sides of the equation by -3, resulting in -3x = 12.
However, the friend did not fully solve for x, resulting in an incorrect solution.
The correct steps to solve the equation were not followed, leading to an incorrect answer.