EQUATIONS WITH VARIABLES ON BOTH SIDES

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the equation contains variables (like x or y) on both the left and right sides, which need to be isolated to solve for the variable.

Front

How do you isolate a variable in an equation with variables on both sides?

Back

You can isolate a variable by performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the equation to get the variable on one side.

Front

What is the first step in solving the equation 5w + 5 = 8w - 10?

Back

The first step is to subtract 5w from both sides to start isolating the variable w.

Front

What is the next step after simplifying the equation -3w = -15?

Back

The next step is to divide both sides by -3 to solve for w.

Front

In the equation -11b + 8 = -3, what operation should be performed first?

Back

You should subtract 8 from both sides to begin isolating b.

Front

What is the solution to the equation 4(x - 2) = -3 + 5x?

Back

The solution is x = -5.

Front

How do you solve the equation 3 + a/3 = 6 for a?

Back

First, subtract 3 from both sides to get a/3 = 3, then multiply both sides by 3 to find a = 9.

Front

What is the final answer for the equation 24 = 2a - 6?

Back

The final answer is a = 15.

Front

What is the importance of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming that it is correct.

Front

What does it mean to perform inverse operations in solving equations?

Back

Inverse operations are operations that undo each other, such as addition and subtraction or multiplication and division, used to isolate variables.