PF Flashcard 8 (Linear Eqns & Ineqs)

Front

What is the solution to the equation 5x = (x + 6)/3?

Back

x = 3/7

Front

How do you express the inequality 6 < x < 10 in interval notation?

Back

(6, 10]

Front

What is the solution to the inequality 1 < 3x + 4?

Back

x > -1

Front

What does it mean when the solution to an equation is 'all real numbers'?

Back

It means that any real number can satisfy the equation.

Front

How can you express 'x is less than 7' in interval notation?

Back

(-∞, 7)

Front

What is the first step in solving the equation 3(2x + 1) - x = 5x + 3?

Back

Distribute 3 to (2x + 1) to simplify the left side.

Front

What is the definition of an inequality?

Back

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

Front

What does the interval notation (a, b) represent?

Back

It represents all numbers x such that a < x < b, excluding a and b.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the endpoints, while non-strict inequalities (≤, ≥) do include the endpoints.

Front

How do you solve for x in the equation 5x + 3 = 2x + 12?

Back

Isolate x by moving all terms involving x to one side and constant terms to the other.