Unit 3 (Expressions, Equations, and Inequalities) Review

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

How do you solve the equation -5(3x + 2) + 4x = 0?

Back

First, apply the distributive property: -15x - 10 + 4x = 0. Combine like terms: -11x - 10 = 0. Then, isolate x: -11x = 10, so x = -10/11.

Front

What does GCF stand for and how is it used in factoring?

Back

GCF stands for Greatest Common Factor. It is the largest factor that divides two or more numbers. In factoring, it is used to simplify expressions by factoring out the GCF.

Front

How do you factor the expression 5x + 35?

Back

Identify the GCF, which is 5. Factor it out: 5(x + 7).

Front

What is the solution to the equation r - 11 = 5?

Back

To solve for r, add 11 to both sides: r = 5 + 11, so r = 16.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you graph the inequality a ≥ 11?

Back

To graph a ≥ 11, draw a solid line at a = 11 and shade the region above the line, indicating all values of a that are greater than or equal to 11.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What is the first step in solving a linear equation?

Back

The first step is to isolate the variable on one side of the equation, often by using inverse operations.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.