Solve this inequality 14x less than or equal to 10000 and choose the graph of the solution, round to the nearest dollar. Show your work
To solve the inequality 14x ≤ 10000, we divide both sides of the inequality by 14:
14x/14 ≤ 10000/14
Simplifying:
x ≤ 714.29
Rounding to the nearest dollar, x ≤ $714.
The graph of the solution is a closed circle at x = 714, with all values less than or equal to 714 shaded to the left of the circle.
To solve the inequality "14x ≤ 10000," we will divide both sides of the inequality by 14 to isolate the variable x. Here's the step-by-step process:
1. Start with the inequality: 14x ≤ 10000.
2. Divide both sides of the inequality by 14: (14x)/14 ≤ 10000/14.
This simplifies to: x ≤ 714.2857.
3. Since we need to round to the nearest dollar, we round x down to the nearest whole number because the inequality is "less than or equal to."
Rounded down, x ≤ 714.
Now, let's graph the solution on the number line:
- Start by drawing a number line with values extending from negative infinity to positive infinity.
- Locate and mark the value x = 714 with a closed circle.
- Shade the region to the left of the closed circle, since the inequality is x ≤ 714.
- Finally, indicate the direction of the shading with an arrow.
The graph of the solution will have a closed circle at 714, a shaded region to the left, and an arrow pointing towards the left.
To solve the inequality "14x ≤ 10000," we need to isolate the variable x.
Divide both sides of the inequality by 14:
14x/14 ≤ 10000/14
x ≤ 714.29 (rounded to the nearest hundredth)
So, the solution to the inequality is x ≤ 714.29.
To graph this solution, we draw a number line and mark the point 714.29 on it. Then, shade the entire region to the left of this point since x is less than or equal to 714.29.
The graph of the solution is as follows:
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... | | | | | A
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0 X X X X X
In the graph, the shaded region to the left of the point A represents the solution x ≤ 714.29.