Rene used a $4 off coupon to buy bows which cost $2 each. Write an inequality rene could use to determine the number of bows she can buy if she plans to spen more that $8. Then graph the solution set
cost = 2 n- 4
2n-4 > 8
2 n > 12
n > 6
To write the inequality, let's first consider the total cost of the bows Rene buys. Since each bow costs $2, and she plans to buy a certain number of bows, let's represent the number of bows as "x". Therefore, the total cost, including the $4 off coupon, can be calculated as:
Total Cost = Number of Bows * Cost per Bow - Coupon Amount
Total Cost = 2x - 4
Now, we want to find the number of bows that Rene can buy if she plans to spend more than $8. This can be represented by the following inequality:
2x - 4 > 8
To solve this inequality and find the values of "x" that satisfy it, we can add 4 to both sides of the inequality:
2x - 4 + 4 > 8 + 4
2x > 12
Finally, to isolate "x", we can divide both sides of the inequality by 2:
2x/2 > 12/2
x > 6
Therefore, the inequality that represents the number of bows Rene can buy if she plans to spend more than $8 is:
x > 6
To graph the solution set, we can plot all values of "x" greater than 6 on a number line. Since the inequality is strict (x > 6), we use an open circle at 6 and shade the area to the right of it:
-------------------->
0 1 2 3 4 5 6 7 8 9 ...
To determine the number of bows Rene can buy, let's represent the number of bows as "x".
The cost of each bow is $2, so the total cost of buying "x" bows will be 2x.
Rene used a $4 off coupon, which means the amount she will actually spend is the total cost minus the coupon value, which is 2x - 4.
Rene plans to spend more than $8, so we can set up the inequality:
2x - 4 > 8
To graph the solution set, we first need to solve the inequality for "x":
2x - 4 > 8
2x > 8 + 4
2x > 12
x > 6
The solution set for this inequality is x > 6.
To graph this solution set, we draw an open circle at x = 6, then shade the region to the right of 6 on the number line, indicating all values greater than 6 are solutions.
Here is the graph of the solution set:
|
-------------o--+---------------> x
6|