Equations - Variables on both sides

What is the solution to the equation -2y + 8 = 4y - 10?

• y = 1

• y = 2

• y = 3

• y = 4

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

• To add complexity to the equation

• To create new variables

• To undo operations and isolate the variable

• To make the equation more difficult to solve

What is the solution to the equation 3x = 15 - 2x?

• x = 1

• x = 2

• x = 3

• x = 4

How do you isolate a variable in an equation?

• By adding the same number to both sides of the equation.

• By performing inverse operations to get the variable on one side of the equation.

• By multiplying both sides by the variable.

• By dividing both sides by the coefficient of the variable.

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

• To multiply different terms in an equation.

• To simplify the equation by adding or subtracting terms that have the same variable and exponent.

• To rearrange the equation in a different order.

• To eliminate all variables from the equation.

What is the general form of a linear equation?

• Ax + By = C, where A, B, and C are constants.

• y = mx + b, where m is the slope and b is the y-intercept.

• y = ax^2 + bx + c, where a, b, and c are constants.

• Ax^2 + By^2 = C, where A, B, and C are constants.

What is the solution to the equation -38 + 6x = 52 + 3x?

• x = 10

• x = 20

• x = 30

• x = 40

What is the importance of maintaining balance in an equation?

• It allows for the simplification of complex equations.

• It ensures that whatever operation you perform on one side of the equation, you must perform on the other side to keep the equation true.

• It helps in finding the roots of the equation more easily.

• It is only necessary for linear equations.

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

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

• Multiply both sides of the equation by the same number.

• Add the same value to both sides of the equation.

• Graph the equation and see if the solution lies on the line.

What is the solution to the equation -7x - 36 = 20 - 3x?

• x = -10

• x = -14

• x = 5

• x = 8