Solving Literal Equations

Front

What is a literal equation?

Back

A literal equation is an equation that contains two or more variables. It is often solved for one variable in terms of the others.

Front

How do you isolate a variable in a literal equation?

Back

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

Front

What is the first step to solve the equation 8x + 4y = 16 for y?

Back

Subtract 8x from both sides to get 4y = 16 - 8x.

Front

What is the solution for y in the equation 8x + 4y = 16?

Back

The solution is y = -2x + 4.

Front

What does it mean to solve for x in an equation?

Back

To solve for x means to manipulate the equation to express x in terms of other variables or constants.

Front

Given the equation x = by + v, how do you isolate x?

Back

x is already isolated; it is expressed in terms of y and v.

Front

What is the formula for solving for b in the equation P = a + (n - 1)b?

Back

The formula is b = \frac{P - a}{n - 1}.

Front

What is the first step to solve the equation P = a + (n - 1)b for b?

Back

Subtract a from both sides to get P - a = (n - 1)b.

Front

In the equation P = a + (n - 1)b, what does (n - 1) represent?

Back

(n - 1) represents the number of intervals or segments in a sequence.

Front

What is the purpose of rearranging equations?

Back

Rearranging equations allows us to express one variable in terms of others, making it easier to solve for specific variables.