Solving Equations

Front

What is the first step to solve the equation 7(1 + 2n) = -105?

Back

Distribute the 7 to both terms inside the parentheses.

Front

How do you isolate the variable in the equation -119 = 1 - 6(3n - 4)?

Back

First, simplify the right side by distributing -6, then move constants to one side and the variable terms to the other.

Front

What is the solution to the equation -11 + 3(b + 5) = 7?

Back

The solution is b = 1.

Front

What does the equation 0 = 8z + 8 imply about the value of z?

Back

It implies that z = -1.

Front

How do you solve the equation -87 = -3(3r + 8)?

Back

Distribute -3, then isolate r by moving constants to one side.

Front

What is the purpose of distributing in an equation?

Back

To eliminate parentheses and simplify the equation for easier solving.

Front

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

Back

To manipulate the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the significance of checking your solution after solving an equation?

Back

To ensure that the solution satisfies the original equation.

Front

What is the general form of a linear equation?

Back

A linear equation can be expressed as ax + b = c, where a, b, and c are constants.

Front

How can you verify if two equations are equivalent?

Back

By manipulating one equation to see if it can be transformed into the other.