Question

1. which point is a solution of the inequality ( y > -x + 3 )?

a ( (0, 3) )
b ( (1, 4) )
c ( (-1, 4) )
d ( (0, -3) )

1. which inequality is represented by the graph at right?

f ( 2x + y geq 3 )
h ( 2x + y leq 3 )
g ( 2x + y > 3 )
j ( 2x + y < 3 )

1. which of the following describes the graph of ( 3 leq x )?

a the boundary line is dashed, and the shading is to the right.
b the boundary line is dashed, and the shading is to the left.
c the boundary line is solid, and the shading is to the right.
d the boundary line is solid, and the shading is to the left.

Explanation:

Question 43

Step1: Test point (0,3)

Substitute $x=0, y=3$ into $y > -x + 3$:
$3 > -0 + 3 \implies 3 > 3$ (False)

Step2: Test point (1,4)

Substitute $x=1, y=4$ into $y > -x + 3$:
$4 > -1 + 3 \implies 4 > 2$ (True)

Step3: Verify other points (optional)

For $(-1,4)$: $4 > 1 + 3 \implies 4 > 4$ (False)
For $(0,-3)$: $-3 > -0 + 3 \implies -3 > 3$ (False)

Step1: Identify boundary line

The graph has a solid line, so the inequality uses $\leq$ or $\geq$. The line passes through $(0,3)$ and $(1.5,0)$, so its equation is $2x + y = 3$.

Step2: Test shading region

Test the origin $(0,0)$: $2(0)+0=0 \leq 3$, and $(0,0)$ is in the shaded region.

Step1: Analyze boundary line

The inequality $3 \leq x$ (or $x \geq 3$) uses $\geq$, so the boundary line $x=3$ is solid.

Step2: Determine shading direction

For $x \geq 3$, values greater than 3 lie to the right of the vertical line $x=3$, so shading is to the right.

Answer:

B. (1, 4)

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Question 44