a. Let's set up the equation to represent the situation:
\[x/2 + 3 = 15\]
To solve for x, we'll first subtract 3 from both sides of the equation:
\[x/2 = 12\]
Then, multiply both sides by 2 to get rid of the fraction:
\[x = 24\]
Therefore, the original number of colored pencils in your box was 24.
b. To have at least 20 colored pencils left in your box, we can set up the inequality:
\[x/2 + 3 \geq 20\]
Subtracting 3 from both sides gives:
\[x/2 \geq 17\]
Then, multiplying both sides by 2:
\[x \geq 34\]
Therefore, you would have needed at least 34 colored pencils originally.
c. The inequality for this situation would be:
\[x/2 + 3 \leq 15\]
Subtracting 3 from both sides:
\[x/2 \leq 12\]
Multiplying both sides by 2:
\[x \leq 24\]
Thus, the possible range for the original number of colored pencils is x ≤ 24.
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.
3 answers
are the [ and / nessesary?
No, the brackets [ ] and forward slash / are not necessary in this case. They were used to help separate and clarify the different parts of the equations, but the equations can be written without them. Here are the revised equations without the brackets and forward slash:
a. Equation: x/2 + 3 = 15
Solution: Subtract 3 from both sides: x/2 = 12
Multiply both sides by 2: x = 24
b. Inequality: x/2 + 3 ≥ 20
Solution: Subtract 3 from both sides: x/2 ≥ 17
Multiply both sides by 2: x ≥ 34
c. Inequality: x/2 + 3 ≤ 15
Solution: Subtract 3 from both sides: x/2 ≤ 12
Multiply both sides by 2: x ≤ 24
These equations and inequalities can be expressed without the brackets and forward slash, but they were used initially to make it clearer.
a. Equation: x/2 + 3 = 15
Solution: Subtract 3 from both sides: x/2 = 12
Multiply both sides by 2: x = 24
b. Inequality: x/2 + 3 ≥ 20
Solution: Subtract 3 from both sides: x/2 ≥ 17
Multiply both sides by 2: x ≥ 34
c. Inequality: x/2 + 3 ≤ 15
Solution: Subtract 3 from both sides: x/2 ≤ 12
Multiply both sides by 2: x ≤ 24
These equations and inequalities can be expressed without the brackets and forward slash, but they were used initially to make it clearer.