Unit 4 Study Guide – Solving Equations & 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. Examples include: x > 5, y ≤ 10.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves shading a region of the graph that represents all the solutions to the inequality. For example, for x > 3, you would shade to the right of 3.

Front

What is the solution to the equation 3(2x - 5) = 4x + 6 + 2x?

Back

The solution is no solution, as the equation simplifies to a false statement.

Front

How do you find the average of a set of numbers?

Back

To find the average, sum all the numbers and divide by the count of the numbers. For example, the average of 67, 55, and 70 is (67 + 55 + 70) / 3.

Front

What is the formula for solving for y in the equation 3x + 4y = 8?

Back

Front

What does it mean if a variable is greater than zero?

Back

If a variable is greater than zero (e.g., a > 0), it means that the value of the variable is positive.

Front

How do you interpret the solution x < 15 weeks in a real-world context?

Back

It means that you can withdraw money for less than 15 weeks while still having more than $50 left in your account.

Front

What is the significance of the term 'no solution' in an equation?

Back

'No solution' means that there are no values for the variable that can satisfy the equation.

Front

What is the process for solving inequalities?

Back

To solve inequalities, isolate the variable using similar steps as solving equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.