Solving Equations and Inequalities

Front

What is 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. For example, x < 5 means x is less than 5.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true. For example, in the equation 2x + 3 = 7, solving for x gives x = 2.

Front

What is the solution to the inequality -2x - 4 ≤ 11?

Back

x ≥ -7.5.

Front

What is the solution to the equation 2x - 14 = 6?

Back

x = 10.

Front

How do you represent a real-world problem as an equation?

Back

Identify the quantities involved, assign variables, and translate the relationships into an equation. For example, if Ainsley bought shirts for $15 each and received $50 off, the equation is 15x - 50 = 400.

Front

What is the purpose of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming its correctness.

Front

What is a variable in mathematics?

Back

A variable is a symbol, often a letter, that represents an unknown value in an equation or expression.

Front

What does it mean for an equation to be balanced?

Back

An equation is balanced when both sides have the same value. For example, in 2x + 3 = 7, both sides equal 7 when x = 2.

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

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation. For example, in 2x + 3 = 7, subtract 3 from both sides and then divide by 2.