solving equations

Front

What is the first step in solving the equation 4 - 2(x - 3) = 24?

Back

Distribute the -2 to both terms inside the parentheses: 4 - 2x + 6 = 24.

Front

How do you isolate the variable x in the equation 2x - 3 + 4x = 27?

Back

Combine like terms (2x + 4x = 6x) to get 6x - 3 = 27, then add 3 to both sides and divide by 6.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that the equation is true for all values of the variable, often resulting from equivalent expressions.

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Front

What is the purpose of combining like terms in an equation?

Back

To simplify the equation, making it easier to isolate the variable.

Front

What does it mean to distribute in an equation?

Back

To multiply a term outside the parentheses by each term inside the parentheses.

Front

What is the solution to the equation 3x + 15 = 3(x + 5)?

Back

Both sides simplify to 3x + 15 = 3x + 15, indicating infinitely many solutions.

Front

What is the first step to solve the equation 4x + 8 = 32?

Back

Subtract 8 from both sides to isolate the term with x.

Front

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

Back

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