Multi-Step Equations (Regents)

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

Front

How do you solve the equation: 15x − 3(3x + 4) = 6?

Back

1. Distribute: 15x - 9x - 12 = 6 2. Combine like terms: 6x - 12 = 6 3. Add 12 to both sides: 6x = 18 4. Divide by 6: x = 3.

Front

What is the formula for simple interest?

Back

The formula for simple interest is I = P * r * t, where I is the interest, P is the principal amount, r is the rate of interest, and t is the time.

Front

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

Back

To solve for r, rearrange the formula to r = I / (P * t).

Front

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

Back

Isolating a variable means manipulating the equation to get the variable on one side by itself, making it easier to solve.

Front

If 3(a - 2) = 5m - 6 + 2a, how do you find a in terms of m?

Back

1. Distribute: 3a - 6 = 5m - 6 + 2a 2. Combine like terms: a - 6 = 5m - 6 3. Add 6 to both sides: a = 5m.

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 consecutive integers?

Back

Let the smallest integer be x. Then the next two consecutive integers can be represented as x + 1 and x + 2.

Front

What is the solution to the equation: \frac{2x}{3} + \frac{x}{6} = 5?

Back

1. Find a common denominator: \frac{4x}{6} + \frac{x}{6} = 5 2. Combine: \frac{5x}{6} = 5 3. Multiply by 6: 5x = 30 4. Divide by 5: x = 6.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.