The equation y = −2x + 3 is the boundary line for the inequality y ≤ −2x + 3. Which sentence describes the graph of the inequality? The region shaded below a dashed boundary line. The region shaded above a solid boundary line. The region shaded below a solid boundary line. The region shaded above a dashed boundary line.
2nd one x=6 or above
The point-slope form of the equation of the line is:
Where m is the slope and b is the intersection with the y-axis.
In the line , you can identify that:
The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).
Then the answer is the option C.
2. 8≥ 3 x + 5
⇒ 3 ≥ 3 x
Dividing both sides by 3
1≤ x or x ≥ 1 is the solution of above inequality.i.e x∈[1,0).
The solution of the above inequality is that x lies in the interval from 0 to 1 represented as 0≤x<1.
3. -2 x + 3 > 3(2 x - 1)
⇒ -2 x + 3> 3× 2 x - 3× 1 ⇒ [using distributive property which is a(b+c)=a×b + a× c]
⇒-2 x - 6 x > -3-3 →[ Bringing like terms together]
⇒ - 8 x > -6
Cancelling negative sign from both sides
if ,-a>-b, then a<b.
⇒8 x< 6
The solution of the above inequality is x should be less than three by four.
C. The region shaded below a solid boundary line.
The given inequality is
The boundary line for this inequality is .
Since the inequality involve , we use a solid boundary line.
After graphing the boundary line; we test the origin to determine which half -plane to be shaded. This is because the boundary lie is not passing through the origin.
Testing the origin yields .
This implies that; . This statement is true.
Hence we shade the lower half-plane of the solid boundary line.
The correct choice is C.
≤ means all the point lies on the curve and below that curve
since here its linear inequality and
y =-2x+3 is linear equation.
All the point lies on y =-2x+3 and below this line describes the region shown by this inequality