You originally have x colored pencils in your pencil box. You share them equally between you and your friend. You add in 3 more colored pencils to your own box after sharing them. This gives you a total of 15 pencils.
a. Write an equation and show all of your steps for solving x (the original number of colored pencils in your box).
b. If you wanted to have at least 20 colored pencils left in your box, how many colored pencils would you have needed originally?
c. Write an inequality and show all steps for solving for x.
a. Let's set up the equation:
(x/2) + 3 = 15
First, divide both sides of the equation by 2 to isolate the x term:
(x/2) = 15 - 3
Simplify to get:
(x/2) = 12
Then, multiply both sides of the equation by 2 to solve for x:
x = 24
So, the original number of colored pencils in your box was 24.
b. To have at least 20 colored pencils left in your box, you would need to set up the inequality:
(x/2) + 3 ≥ 20
First, subtract 3 from both sides of the equation:
(x/2) ≥ 20 - 3
Simplify to get:
(x/2) ≥ 17
Then, multiply both sides of the equation by 2 to solve for x:
x ≥ 34
So, you would have needed at least 34 colored pencils originally to have at least 20 left in your box.
c. The inequality is x/2 + 3 ≤ 15.
First, subtract 3 from both sides of the equation:
x/2 ≤ 12
Then, multiply both sides of the equation by 2 to solve for x:
x ≤ 24
So, the original number of colored pencils in your box must be 24 or less.
Solve the equation filling in the steps: 2(x−3)+21=−3
Distribute to get
Combine like terms to get Response area
Use the (choose a property) Response area to get (resulting equation)
Use the (choose a property) to get (resulting answer)
Distribute to get 2x - 6 + 21 = -3.
Combine like terms to get 2x + 15 = -3.
Subtract 15 from both sides to isolate the x term: 2x = -18.
Divide both sides by 2 to solve for x: x = -9.
Using the property of subtraction, subtract 6 from both sides to get 2x = -18.
Using the property of division, divide both sides by 2 to get x = -9.
a. Let's solve the equation step by step:
Step 1: Start with x colored pencils in your box.
Step 2: Share them equally between you and your friend, so each of you gets x/2 colored pencils.
Step 3: Add 3 more colored pencils to your own box, so you have x/2 + 3 colored pencils in your box.
Step 4: The total number of colored pencils after sharing is x/2 + 3 + x/2 (from you and your friend), which should equal 15.
Step 5: Simplify the equation: (x/2 + x/2) + 3 = 15.
Step 6: Combine like terms: x/2 + x/2 + 3 = 15.
Step 7: Simplify further: 2(x/2) + 3 = 15.
Step 8: Distribute: x + 3 = 15.
Step 9: Subtract 3 from both sides: x + 3 - 3 = 15 - 3.
Step 10: Simplify: x = 12.
Therefore, the original number of colored pencils in your box was 12.
b. To determine the original number of colored pencils needed to have at least 20 left, let's solve the equation step by step:
Step 1: Let's assume the original number of colored pencils in your box is x.
Step 2: Share them equally between you and your friend, so each of you gets x/2 colored pencils.
Step 3: After sharing, you add 3 more colored pencils to your own box, so you have x/2 + 3 colored pencils in your box.
Step 4: The total number of colored pencils after sharing is x/2 + 3 + x/2, which should be greater than or equal to 20.
Step 5: Write the inequality: x/2 + 3 + x/2 ≥ 20.
Step 6: Simplify the inequality: (x + x)/2 + 3 ≥ 20.
Step 7: Combine like terms: (2x/2) + 3 ≥ 20.
Step 8: Simplify further: x + 3 ≥ 20.
Step 9: Subtract 3 from both sides: x + 3 - 3 ≥ 20 - 3.
Step 10: Simplify: x ≥ 17.
Therefore, the original number of colored pencils needed to have at least 20 left in your box is 17.