Solving Equations

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means manipulating the equation to get the variable on one side of the equation by itself.

Front

What is the first step to solve the equation 8(7-y) = -24?

Back

Distribute the 8 to both terms inside the parentheses: 56 - 8y = -24.

Front

How do you solve for y in the equation 8(7-y) = -24?

Back

First, distribute: 56 - 8y = -24. Then, subtract 56 from both sides: -8y = -80. Finally, divide by -8: y = 10.

Front

What operation should you perform to solve x - 62 = 123?

Back

Add 62 to both sides to isolate x.

Front

What is the solution to the equation n + 2 = -14 - n?

Back

Combine like terms: 2n + 2 = -14. Then, subtract 2 from both sides: 2n = -16. Finally, divide by 2: n = -8.

Front

How do you solve the equation -6w + 1 = -11?

Back

Subtract 1 from both sides: -6w = -12. Then, divide by -6: w = 2.

Front

What is the solution to the equation 6 - 3a = 21?

Back

Subtract 6 from both sides: -3a = 15. Then, divide by -3: a = -5.

Front

What does it mean to check your solution in an equation?

Back

To check your solution, substitute the value back into the original equation to verify that both sides are equal.

Front

What is the purpose of using inverse operations in solving equations?

Back

Inverse operations are used to undo operations performed on a variable, helping to isolate it.