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 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 5(6 + 3r) + 7 = 127?

Back

First, simplify: 30 + 15r + 7 = 127. Then, combine like terms: 15r + 37 = 127. Subtract 37 from both sides: 15r = 90. Finally, divide by 15: r = 6.

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.

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

Back

x < 3.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary value, while a non-strict inequality (≤ or ≥) does include the boundary value.

Front

How do you check if a 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 -8x - 8 + 3x - 6 = -3x + 2?

Back

x = -8.

Front

What does it mean to have all real numbers as a solution?

Back

It means that any value for the variable will satisfy the equation or inequality.