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 isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

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.

Front

What is the first step in solving the equation 4k + 24 = 6k - 10?

Back

The first step is to move all terms involving k to one side and constant terms to the other side.

Front

Solve: 4k + 24 = 6k - 10. What is k?

Back

k = 17.

Front

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

Back

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

Front

What is the error in the following steps? 19 - 2k = 3k - 1; +3k; 19 + 1k = -1; -19; k = -20.

Back

Instead of adding 3k, they should subtract 3k.

Front

Solve: 5x + 15 = 10x - 40. What is x?

Back

x = 11.

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.