First consider the system of equations y= -1/2x + 1 and y = x - 5. Then consider the system of inequalities y > -1/2x + 1 and
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Use y = mx + b to determine the equation of the graph, then decided the inequality symbol.
m = +5/+6 = b = 5
y = x + 5
6y = 5x + 30
-30 = 5x - 6y ⇒ 5x - 6y = -30
Now let's look at the inequality symbol: The shaded area is below so it will be a less than symbol and it is a solid line so the equal sign is included.
Answer: 5x - 6y ≤ -30
We can begin by rearranging this into multiplication:
Now we can factor the numerators and denominators:
The factors (x+4) and (x+2) cancel out, leaving us with:
Our answer comes out to be:
Based on the numerator of the second fraction (since we used its inverse), the denominators of both, and the factors we canceled out earlier, the restrictions are x ≠ -4, -3, -2, -1, 4