Solve linear equations with variables on both sides

Front

What is a linear equation?

Back

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What does it mean to solve an equation with variables on both sides?

Back

It means to isolate the variable by performing operations to both sides of the equation until the variable is alone on one side.

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What is the first step in solving the equation 4(3r + 4) = −8(2r + 5)?

Back

Distribute the numbers outside the parentheses: 12r + 16 = -16r - 40.

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What does 'no solution' mean in the context of linear equations?

Back

'No solution' means that there is no value for the variable that satisfies the equation, often resulting in a contradiction.

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What does 'all real numbers' mean as a solution?

Back

'All real numbers' means that any value for the variable will satisfy the equation, indicating that the equation is true for every real number.

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How do you check if your solution to a linear equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

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What is the solution to the equation 6(y - 2) = 6 + 9(y - 2)?

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The solution is 0, indicating that the equation is true for all values of y.

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What is the process of isolating a variable in an equation?

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It involves using inverse operations to get the variable by itself on one side of the equation.

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What is the solution to the equation 2(7r - 4) = 10r - 3?

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What does it mean if an equation has infinite solutions?

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It means that there are countless values for the variable that satisfy the equation, often resulting in equivalent expressions.