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 and shows that one is greater than, less than, or not equal to the other.

Front

How do you solve the equation 4x + 2(x - 6) = 12?

Back

x = 4

Front

What does it mean to isolate a variable in an equation?

Back

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

Front

What is the first step in solving the inequality 5(6 + 3r) + 7 ≥ 127?

Back

Distribute 5 to both terms inside the parentheses: 30 + 15r + 7 ≥ 127.

Front

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

Back

x < 3

Front

Identify the error in the equation 19 - 2k = 3k - 1: +3k +3k leads to 19 + 1k = -1.

Back

Instead of adding 3k, they should subtract 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 equation 5x + 34 = -2(-7x + 1)?

Back

x = 4

Front

What does it mean when an inequality has a 'greater than or equal to' sign?

Back

It means that the value can be either greater than or exactly equal to the number on the other side of the inequality.