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.
. Write an inequality and show all steps for solving for x
Let's first write the inequality for the given information:
(x/2) + 3 + (x/2) = 15
Now, let's solve this inequality step by step:
Multiply 2 to both sides of the equation to eliminate the denominators:
2 * [(x/2) + 3 + (x/2)] = 2 * 15
x + 6 + x = 30
Combine like terms:
2x + 6 = 30
Subtract 6 from both sides of the equation:
2x + 6 - 6 = 30 - 6
2x = 24
Divide both sides of the equation by 2:
(2x)/2 = 24/2
x = 12
Therefore, the original number of colored pencils in the pencil box was 12.
Let's denote the number of colored pencils you originally had in your pencil box as x.
Step 1: Share them equally with your friend
After sharing the pencils equally, both you and your friend have received x/2 colored pencils.
Step 2: Add 3 more colored pencils to your own box
After adding 3 colored pencils to your own box, you have a total of (x/2) + 3 colored pencils.
Step 3: Total pencils after sharing and adding
According to the question, the total number of pencils you have after sharing and adding is 15. So, we can set up the inequality:
(x/2) + 3 = 15
Step 4: Solve for x
To solve for x, we'll isolate the term with x by subtracting 3 from both sides of the equation:
(x/2) + 3 - 3 = 15 - 3
(x/2) = 12
Step 5: Multiply both sides of the equation by 2 to get rid of the fraction:
2 * (x/2) = 12 * 2
x = 24
Therefore, you originally have 24 colored pencils in your pencil box.