Multi-Step Equations (Regents)

Front

What is the formula for simple interest?

Back

Front

How do you rearrange the simple interest formula to solve for the interest rate (r)?

Back

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

How do you determine if an equation has one solution, infinite solutions, or no solution?

Back

You can determine this by simplifying the equation. If you end up with a true statement (like 0=0), it has infinite solutions. If you get a false statement (like 0=5), it has no solution. If you find a specific value for the variable, it has one solution.

Front

What are consecutive integers?

Back

Consecutive integers are integers that follow each other in order, such as 1, 2, 3 or 14, 15, 16.

Front

How do you set up an equation for a word problem involving consecutive integers?

Back

Let the smallest integer be x. Then the next two consecutive integers can be expressed as x+1 and x+2. You can then set up an equation based on the problem's conditions.

Front

What is the solution to the equation 15x − 3(3x + 4) = 6?

Back

The solution is x = 3.

Front

How do you solve a multi-step equation?

Back

To solve a multi-step equation, first simplify both sides if possible, then isolate the variable by performing inverse operations.

Front

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

Back

Isolating a variable means to manipulate the equation so that the variable is on one side of the equation by itself.

Front

What is the first step in solving the equation 3(a - 2) = 5m - 6 + 2a?

Back

The first step is to distribute the 3 on the left side, resulting in 3a - 6 = 5m - 6 + 2a.