I NEED HELP !
Match the inequality to its graph.
A. less than or equal to -1
B. less than 3
C. less than 1
D. less than or equal to -3
7. 4y + 3 *less than or equal to* y+6
8. -2y > 2
9. y over 3 < -1
10. 3y *less than or equal to* 2y +3
7. C
8. A
9. D
10. B
glad if this helps ya! :D
To match the inequalities to their respective graphs, we need to solve each inequality step-by-step.
7. 4y + 3 ≤ y + 6:
- First, let's simplify the inequality by combining like terms.
3y + 3 ≤ 6
- Next, subtract 3 from both sides to isolate y.
3y ≤ 3
- Now, divide both sides by 3 to solve for y.
y ≤ 1
The graph for the inequality y ≤ 1 is a solid line that is shaded below the line.
8. -2y > 2:
- Begin by dividing both sides of the inequality by -2. Remember to flip the inequality sign since we are dividing by a negative number.
y < -1
The graph for the inequality y < -1 is an open circle at -1 on the number line, shaded to the left.
9. y/3 < -1:
- Multiply both sides of the inequality by 3 to get rid of the fraction.
y < -3
The graph for the inequality y < -3 is an open circle at -3 on the number line, shaded to the left.
10. 3y ≤ 2y + 3:
- Subtract 2y from both sides to isolate y.
y ≤ 3
The graph for the inequality y ≤ 3 is a solid line that is shaded below the line.
Now, let's match the inequalities to their corresponding graphs:
A. Graph for "less than or equal to -1": y ≤ 1
B. Graph for "less than 3": y < -1
C. Graph for "less than 1": y < -3
D. Graph for "less than or equal to -3": y ≤ 3
To match each inequality with its graph, we can solve each inequality and then analyze the solutions. Here's how you can solve each inequality and find the corresponding graph:
7. 4y + 3 ≤ y + 6:
First, simplify the inequality:
4y + 3 ≤ y + 6
Combine like terms:
3y + 3 ≤ 6
Subtract 3 from both sides:
3y ≤ 3
Divide both sides by 3:
y ≤ 1
This inequality represents all values of y that are less than or equal to 1. To graph this, you would draw a solid horizontal line at y = 1 and shade the region below the line.
8. -2y > 2:
First, simplify the inequality:
-2y > 2
Divide both sides by -2 (note that dividing by a negative number flips the inequality sign):
y < -1
This inequality represents all values of y that are less than -1. The graph would be a dashed horizontal line at y = -1, with the region below the line left unshaded.
9. y/3 < -1:
First, simplify the inequality:
y/3 < -1
Multiply both sides by 3 (since we're dividing by a positive number, the inequality sign stays the same):
y < -3
This inequality represents all values of y that are less than -3. The graph would be a dashed horizontal line at y = -3, with the region below the line left unshaded.
10. 3y ≤ 2y + 3:
First, simplify the inequality:
3y ≤ 2y + 3
Subtract 2y from both sides:
y ≤ 3
This inequality represents all values of y that are less than or equal to 3. To graph this, you would draw a solid horizontal line at y = 3 and shade the region below the line.
By solving each inequality and analyzing the solutions, you can match each inequality with its corresponding graph.
well, do you see any graphs here?
and you can drop the words if you use <= for "less than or equal"