Izzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you, and she asks you if she did it correctly.
This is the work she completed:
3t+3−4t≥−5
−t+3≥−5
−t≥−8
t≥8
(2 points)
True False
Izzie made no mistakes in solving this inequality
True – Izzie made no mistakes in solving this inequality
False – Izzie made no mistakes in solving this inequality
Izzie made a mistake going from step 3 to step 4
True – Izzie made a mistake going from step 3 to step 4
False – Izzie made a mistake going from step 3 to step 4
Izzie made a mistake going from step 1 to step 2
True – Izzie made a mistake going from step 1 to step 2
False – Izzie made a mistake going from step 1 to step 2
Izzie forgot to change the inequality symbol to be t≤8
True – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
False – Izzie forgot to change the inequality symbol to be t is less than or equal to 8
Izzie should have had the answer t≤−8
True – Izzie should have had the answer t is less than or equal to negative 8
False – Izzie made no mistakes in solving this inequality
Izzie is trying to solve this inequality: 3(t+1)−4t≥−5
After she solves it, she shows it to you, and she asks you if she did it correctly.
This is the work she completed:
3t+3−4t≥−5
−t+3≥−5
−t≥−8
t≥8
(2 points)
True False
Izzie made no mistakes in solving this inequality
Izzie made a mistake going from step 3 to step 4
Izzie made a mistake going from step 1 to step 2
Izzie forgot to change the inequality symbol to be t≤8
Izzie should have had the answer t≤−8
False – Izzie made a mistake going from step 3 to step 4.
Which graph represents the solutions to this inequality: 5n−3<3(n+1)
To determine which graph represents the solutions to the inequality 5n - 3 < 3(n + 1), we need to solve the inequality and analyze the resulting solution.
Here are the steps to solve the inequality:
5n - 3 < 3(n + 1)
Expanding the brackets:
5n - 3 < 3n + 3
Combine like terms:
5n - 3n < 3 + 3
2n < 6
Divide both sides by 2:
n < 3
This means that the values for 'n' that satisfy the inequality are all numbers less than 3.
Now, let's analyze the graphs to determine which one represents this solution. [Unfortunately, as an AI text-based model, I am unable to visualize or provide graphical representations. Please provide the available graph options, and I will help you analyze them.]
how can i show you the graphs?
I apologize for the confusion. Since we are in a text-based conversation, you won't be able to directly show me the graphs. However, you can describe the available graph options, and I can try to guide you in deciding which graph represents the solutions. You can describe the characteristics of the graphs, such as the shape, the position of the line, or any other distinguishing features.
Graph 5n−3<3(n+1)
Since I am unable to see the graph directly, I will describe the properties to help you determine which graph represents the solution to the inequality 5n - 3 < 3(n + 1).
In this inequality, the left side is 5n - 3, and the right side is 3(n + 1). To graph this inequality, we'll first consider the equation 5n - 3 = 3(n + 1), which represents the boundary or the equality.
Simplifying the equation:
5n - 3 = 3n + 3
2n = 6
n = 3
So, the boundary or the equality line will be a vertical line passing through the point (3, any y-value). This line will divide the coordinate plane into two regions.
Now, for the inequality 5n - 3 < 3(n + 1), we need to determine which side of the line represents the solutions.
To do this, we can choose a test point within one of the regions. Let's try n = 0:
When n = 0:
5(0) - 3 < 3(0 + 1)
-3 < 3
Since -3 is indeed less than 3, the region containing the test point (0, any y-value) satisfies the inequality.
Therefore, the graph representing the solution to the inequality 5n - 3 < 3(n + 1) will be the portion of the coordinate plane on the same side as the test point (0, any y-value) relative to the boundary line (which is a vertical line passing through (3, any y-value)).
I hope this explanation helps you determine which graph represents the given inequality.
Solve the equation and inequality for x.
Part A: Solve the equation showing all steps.
ax−5=18
Part B: Solve the inequality showing all steps.
ax−5>18
Answer these Questions:
1. Describe the number line set up that would show all of the solutions for the inequality in Part B.
2. State the difference between solving an equation and an inequality.