The solution to the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] is [tex]x[/tex] ≥ [tex]1[/tex].
To solve the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] , we need to consider two cases: when the expression inside the absolute value is positive and when it is negative. Here's a step-by-step explanation:
Case 1: |[tex]2x+1[/tex]| ≥ [tex]3[/tex]
Subtract 1 from both sides of the inequality:
[tex]2x + 1 - 1[/tex] ≥ [tex]3 - 1[/tex]
2x ≥ 2
Divide both sides of the inequality by 2:
[tex]$\frac{2x}{2} ≥ \frac{2}{2}$[/tex]
x ≥ 1
Case 2: -([tex]2x+1[/tex]) ≥ [tex]3[/tex]
Multiply both sides of the inequality by -1 (to reverse the inequality):
-[tex]1(2x + 1)[/tex] ≤ [tex]-1(3)[/tex]
-2x - 1 ≤ -3
Add 1 to both sides of the inequality:
[tex]-2x - 1 + 1[/tex] ≤ [tex]-3 + 1[/tex]
-2x ≤ -2
Divide both sides of the inequality by -2 (note that we need to reverse the inequality sign when dividing by a negative number):
[tex]$\frac{-2x}{-2} ≥ \frac{-2}{-2}$[/tex]
x ≥ 1
Combining the solutions from both cases, we have x ≥ 1.
Therefore, the solution to the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] is [tex]x[/tex] ≥ [tex]1[/tex].
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Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? Estimate the total cost of six grocery items if their prices are , , , , , and , by rounding each price to the nearest dollar and then adding.
a.
The estimated total cost of the grocery items is $36.
b.
The actual total cost of the grocery items is $35.82.
How do we calculate?for part a.
We will round each price to the nearest dollar:
$5.12 = $5
$3.07 = $3
$7.11 = $7
$1.67 = $2
$13.18= $13
$5.67 = $6
Summing them up, we have:
$5 + $3 + $7 + $2 + $13 + $6 = $36
the estimated total cost of the grocery items is $36.
for part b.
We will calculate the actual total cost of the grocery items by using a calculator:
$5.12 + $3.07 + $7.11 + $1.67 + $13.18 + $5.67 = $35.82
In conclusion, we will find the actual total cost of the grocery items as $35.82.
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Let P(x) = -50x+20,000x-1,5000,000 represent the profit function for manufacturing a particular model of recreational
vehicle (RV) and x represent the number of RVS produced monthly. Use a compound inequality to state the range of the
number of RVs that need to be sold each month for the company to make a profit.
O 0
100
200
none of the answer choices
O 0
O 100
Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".
To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.
The profit function is given by P(x) = -50x + 20,000x - 1,500,000.
To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:
-50x + 20,000x - 1,500,000 > 0.
Combining like terms, we have:
19,950x - 1,500,000 > 0.
Now, let's solve this inequality for x:
19,950x > 1,500,000.
Dividing both sides by 19,950, we get:
x > 1,500,000 / 19,950.
Simplifying the right side, we have:
x > 75.
The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.
Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".
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A league is a nautical measurement equal to about 3 miles. If a ship travels 2,000 leagues, about how many miles does the ship travel?
Answer: 600000
Step-by-step explanation: just multiply it man
