Solving Equations and Inequalities

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

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 solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division).

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation so that the variable is on one side and all other terms are on the opposite side.

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 each term inside a parenthesis.

Front

Solve: 4x + 2(x - 6) = 12

Back

x = 4

Front

Solve: 2(2x + 3) = -6(x + 9)

Back

x = -6

Front

Solve: 5x + 34 = -2(-7x + 1)

Back

x = 4

Front

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

Back

r ≥ 6

Front

What is a solution set?

Back

A solution set is the set of all values that satisfy a given equation or inequality.