Understanding Equations and Inequalities
What is the meaning of an equals sign?
An equals sign shows that the left and right side of an equation have the same value.
State the inverse operation of multiplication, and the inverse operation of addition.
The inverse operation of multiplication is division.
The inverse operation of addition is subtraction.
Leah wants no more than 20 people at her birthday party. Write an inequality that represents how many friends she could invite.
x≤20x
Why do you perform the same operation to both sides of the equation?
To ensure the left and right side of the equation stay the same value.
State a difference between an inequality and an equation.
Equations show the relationship between two expressions. The left side of an equation is equal to the right side of an equation. Meanwhile, inequalities show that an expression or variable is greater than, less than, or equal to another.
If you were to add a negative number to both sides of an inequality sign, would you have to flip the inequality sign?
No, you only flip the inequality sign when dividing or multiplying by a negative number.
The middle school is giving free shirts to the first 150 students who come to the pep rally. Write an inequality to represent the possible number of students that receive shirts.
x≤150
Liam solves 2x + 5 = 13. Their answer is 3. Did the student get the answer correct? Why?
No, Liam got the answer wrong. The correct answer is 4 because 13-5 is 8. Then, you divide 8 by 2, and the answer is 4.
Why can inequalities have more than one answer or solution?
Inequalities have more than one solution because they represent a range of values that satisfy the condition. Unlike equations, which have a single solution, inequalities allow for multiple numbers that make the statement true.
Make a word problem for this equation: x + 7 = 12 to show why you would have to subtract 7 from both sides.
Sarah has 12 marbles total. 7 of the marbles are blue and the rest are red. How many marbles are red? You would have to subtract 7 from both sides because if you added 7, you would have a total of 18 marbles. 18 marbles is incorrect.
Write a scenario that represents the inequality x>43
I need at least $43 to go to the concert, x represents the amount of money.
A student solves x + 5 greater than 15 and says their answer is 3. Is this correct? Why or why not?
3 is only part of the answer. However, since this is an inequality, the answer is that x is greater than 3. It is not just 3 because there is a range of possible solutions for inequalities.