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 move all terms containing the variable to one side of the equation and constant terms to the other side.

Front

How do you isolate the variable in an equation?

Back

To isolate the variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

What is the solution to the equation 7w + 5 = 3w - 15?

Back

w = -5.

Front

How do you solve the equation 5y + 34 = -2(-7y + 1)?

Back

First, distribute the -2 on the right side, then combine like terms and isolate y to find y = 4.

Front

What is the process for solving the equation 4(1-x) + 3x = -2(x+1)?

Back

Distribute on both sides, combine like terms, and isolate x to find x = -6.

Front

What is the solution to the equation 8x - 8 = -4x + 16?

Back

x = 2.

Front

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

Back

It means that the variable appears on both sides of the equation, requiring manipulation to isolate the variable.

Front

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

Back

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

Front

What is the final solution for the equation s = 40?

Back

The solution is s = 40.