Solving Equations

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What is the first step in solving a simple linear equation like 2x + 3 = 7?
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Subtract 3 from both sides to isolate the term with the variable.
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What does it mean to 'isolate the variable' in an equation?
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It means rewriting the equation so that the variable is alone on one side of the equation.
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Solve the equation: x/4 = 2.
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Multiply both sides by 4 to get x = 8.
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If you have the equation 3(x - 2) = 9, what should you do first?
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Distribute the 3 to both terms inside the parentheses.
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What is the solution to the equation 5x = 20?
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Divide both sides by 5 to find x = 4.
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True or False: You can add the same number to both sides of an equation to maintain balance.
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True.
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How can you check if your solution to an equation is correct?
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Substitute your solution back into the original equation to see if both sides are equal.
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Solve for y: y + 6 = 12.
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Subtract 6 from both sides to find y = 6.
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What operation would you use to solve x - 4 = 10?
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Add 4 to both sides.
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When solving -3x = 9, what should you do?
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Divide both sides by -3 to get x = -3.
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Why do you need to perform the same operation on both sides of an equation?
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To keep the equation balanced and equality true.
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What does 'equation' mean?
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An equation is a statement that two expressions are equal, often containing variables.
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Solve for x in the equation 6 + x = 10.
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Subtract 6 from both sides to get x = 4.
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If you start with 2(x + 3) = 10, what is the first step?
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Divide both sides by 2 to simplify the equation to x + 3 = 5.
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How would you solve the equation 7 - x = 4?
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Subtract 7 from both sides and then multiply both sides by -1 to find x = 3.
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