Solving Equations with variables on both sides

Front

What is the first step in solving an equation with variables on both sides?

Back

The first step is to isolate the variable by moving all terms containing the variable to one side of the equation and constant terms to the other side.

Front

How do you combine like terms in an equation?

Back

You combine like terms by adding or subtracting the coefficients of the same variable or constant terms.

Front

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

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 10x + 9 = 4x - 9?

Back

The solution is x = -3.

Front

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

Back

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

Front

What is the process for solving the equation -5k + 10 = -2k - 14?

Back

First, add 5k to both sides to get 10 = 3k - 14, then add 14 to both sides to get 24 = 3k, and finally divide by 3 to find k = 8.

Front

What is the significance of having variables on both sides of an equation?

Back

It indicates that the equation may have multiple solutions or require careful manipulation to isolate the variable.

Front

What is the solution to the equation 7x - 4 = 3 + 8x?

Back

The solution is x = -7.

Front

How do you handle equations that result in a false statement, such as 0 = 5?

Back

This indicates that there is no solution to the equation.

Front

What does it mean if an equation simplifies to a true statement, such as 0 = 0?

Back

This indicates that there are infinitely many solutions to the equation.