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 on both sides of the equation to get the variable 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 5x + 15 = 10x - 40?

Back

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

Front

What is the solution to the equation 5x + 15 = 10x - 40?

Back

x = 11.

Front

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

Back

The error is that instead of adding 3k, they should have subtracted 3k.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the inequality -3 − 6(4x + 6) > -111?

Back

x < 3.

Front

What does it mean when an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality.