1. 3x+10≥4
a. x≥-2
b. x≤ 2
c. x≤-2
d. x≥ 2 **
2. The tennis team is selling key chains as a fundraiser. If its goal is to raise at least $180, how many key chains must it sell at $2.25 each to meet that goal? Write and solve an inequality.
a. 2.25k≥180;k≥100
b. 180k≥2.25;k≥80
c. 180k≥2.25;k≥150
d. 2.25k≥180;k≥80**
3x+10 >= 4
3x >= -6
x >= -2
(A)
2.25x >= 180
x >= 80
you are correct
1. To solve the inequality 3x + 10 ≥ 4, we can follow these steps:
Step 1: Subtract 10 from both sides to isolate the variable.
3x + 10 - 10 ≥ 4 - 10
This simplifies to:
3x ≥ -6
Step 2: Divide both sides by 3 to solve for x.
3x/3 ≥ -6/3
This simplifies to:
x ≥ -2
Therefore, the correct answer is option a. x ≥ -2.
2. To find the number of key chains the tennis team must sell to meet their goal, we can set up an inequality. Let's call the number of key chains they need to sell "k".
The inequality can be written as:
2.25k ≥ 180
Step 1: Divide both sides of the inequality by 2.25 to isolate the variable.
(2.25k)/2.25 ≥ 180/2.25
This simplifies to:
k ≥ 80
Therefore, the correct answer is option d. 2.25k ≥ 180; k ≥ 80.
To solve these questions, we will go through the steps one by one.
1. 3x + 10 ≥ 4
To find the solution for x, we need to isolate it on one side of the inequality symbol.
Subtracting 10 from both sides, we get:
3x ≥ -6
Dividing both sides by 3, we get the final solution:
x ≥ -2
Therefore, the correct answer is a. x ≥ -2.
2. Let's write and solve an inequality for the second question.
Let's assume the number of key chains the tennis team needs to sell is 'k'.
The price of each key chain is $2.25.
So, the total amount raised by selling 'k' key chains is 2.25k.
Now, we need to set up an inequality to find the minimum number of key chains, 'k', that the team must sell to meet the fundraising goal of at least $180.
The inequality is:
2.25k ≥ 180
To find the solution for 'k':
Divide both sides of the inequality by 2.25:
k ≥ 80
Therefore, the correct answer is d. 2.25k ≥ 180; k ≥ 80.