Understanding Equations and Inequalities

Lesson 29 focuses on solving one-step inequalities by adding or subtracting, building on concepts from lesson 25. The teacher reviews solving equations using addition or subtraction, then transitions to inequalities, explaining the process with examples. The lesson includes graphing inequalities on a number line and concludes with a summary, highlighting the similarities with lesson 25.

What is the main focus of Lesson 29?

• Solving one-step inequalities by adding or subtracting

• Solving quadratic equations

• Solving multi-step equations

• Graphing linear equations

What is the first step in isolating a variable in an equation?

• Multiply both sides by the same number

• Add or subtract to remove constants from the variable

• Divide both sides by the variable

• Switch the sides of the equation

Why is it important to perform the same operation on both sides of an equation or inequality?

• To make calculations easier

• To eliminate variables

• To maintain balance and equality

• To simplify the expression

In the equation m + 7 = -3, what operation is needed to isolate m?

• Add 7 to both sides

• Subtract 7 from both sides

• Divide both sides by 7

• Multiply both sides by 7

What is the key difference between solving equations and inequalities?

• Equations require multiplication, inequalities require division

• Equations have equal signs, inequalities have inequality symbols

• Equations use addition, inequalities use subtraction

• Equations are solved graphically, inequalities are solved algebraically

What does the inequality symbol '>' indicate?

• Less than

• Greater than

• Not equal to

• Equal to

In the inequality x - 5 > 17, what operation is needed to solve for x?

• Subtract 5 from both sides

• Add 5 to both sides

• Multiply both sides by 5

• Divide both sides by 5

What happens if you add 5 to both sides of the inequality x - 5 > 17?

• The inequality becomes x < 22

• The inequality becomes x = 22

• The inequality becomes x > 22

• The inequality becomes x > 12

How is the solution to an inequality represented on a number line?

• With a closed circle and a line

• With an open circle and a line

• With a shaded region

• With a dashed line

What does an open circle on a number line indicate?

• The number is included in the solution

• The number is not included in the solution

• The solution is approximate

• The solution is incorrect