How To Solve Systems of Inequalities Graphically
1) Write the inequality in slope-intercept form or in the form
y
=
m
x
+
b
y=mx+b
.
For example, if asked to solve
x
+
y
≤
10
x+y≤10
, we first re-write as
y
≤
−
x
+
10
y≤−x+10
.
2) Temporarily exchange the given inequality symbol (in this case
≤
≤
) for just equal symbol. In doing so, you can treat the inequality like an equation. BUT DO NOT forget to replace the equal symbol with the original inequality symbol at the END of the problem!
So,
y
≤
−
x
+
10
y≤−x+10
becomes
y
=
−
x
+
10
y=−x+10
for the moment.
3) Graph the line found in step 2. This will form the "boundary" of the inequality -- on one side of the line the condition will be true, on the other side it will not. Review how to graph a line here.
4) Revisit the inequality we found before as
y
≤
−
x
+
10
y≤−x+10
. Notice that it is true when y is less than or equal to. In step 3 we plotted the line (the equal-to case), so now we need to account for the less-than case. Since y is less than a particular value on the low-side of the axis, we will shade the region below the line to indicate that the inequality is true for all points below the line:
5) Verify. Plug in a point not on the line, like (0,0). Verify that the inequality holds. In this case, that means
0
≤
−
0
+
10
0≤−0+10
, which is clearly true. We have shaded the correct side of the line.
Answer:
Selling price should be $21 per unit.
Step-by-step explanation:
Cost price of manual = Fixed price + variable cost per package×Number of units sold
= 780000+19.85×1250000 = $25592500
Now we know Learning center wants a profit = $650000
Then profit = sale price - cost price
650000=sale price - 25592500
Sale price = 650000+25592500 = $26242500
This is the sale price of 1250000 units then selling price per unit should be = Total selling price/Number of units sold
= $26242500/1250000 =20.994 or $21
Selling price should be $21 per unit.
Profit is equal to gains - losses. In this case it would be
100,000-70,000-18,000=profit=$12,000
To solve this problem you must apply the proccedure shown below:
1. You have the following information given in the problem:
-<span>The mass of 4 large zucchini is about 2 kilograms.
2. Then, you have:
1 kilogram-----1000 grams
2 kilograms--..x
x=2x1000/1
x=2000 grams
3. Then, you have:
4 large zucchini----2000 grams
1 large zucchini----x
x=2000/4
x=500 grams
The answer is: 500 grams
</span>
Answer:
2 cans of paint are needed to paint 332 square feet.
