Equations and Inequalities Test

Front

What is the order of operations in mathematics?

Back

The order of operations is a set of rules that dictates the sequence in which calculations are performed. The acronym PEMDAS is commonly used: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Front

What is the imaginary unit 'i'?

Back

Front

Back

Front

What is the solution to the equation 4x + 2(x - 6) = 12?

Back

To solve, first distribute: 4x + 2x - 12 = 12. Combine like terms: 6x - 12 = 12. Add 12 to both sides: 6x = 24. Divide by 6: x = 4.

Front

What does interval notation represent?

Back

Interval notation is a way of writing subsets of the real number line. It uses parentheses and brackets to indicate whether endpoints are included (closed) or excluded (open).

Front

How do you write the inequality x < 5 in interval notation?

Back

In interval notation, x < 5 is written as (-∞, 5).

Front

What is the solution to the inequality 5(6 + 3r) + 7 ≥ 127?

Back

First, simplify: 30 + 15r + 7 ≥ 127. Combine like terms: 15r + 37 ≥ 127. Subtract 37: 15r ≥ 90. Divide by 15: r ≥ 6.

Front

What is a linear equation?

Back

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, less than, or not equal to another.

Front

How do you solve the equation 2x + 3 = 11?

Back

Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.