Question

Which of the following systems of inequalities has point B as a solution?

Two linear functions f of x equals 3 times x plus 4 and g of x equals negative one half times x minus 5 intersecting at one point, forming an X on the page. A point above the intersection is labeled A. A point to the left of the intersection is labeled B. A point below the intersection is labeled C. A point to the right of the intersections is labeled D.

f(x) ≤ 3x + 4
g of x is less than or equal to negative one half times x minus 5
f(x) ≥ 3x + 4
g of x is less than or equal to negative one half times x minus 5
f(x) ≤ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5

Answer 1

B) f(x) ≥ 3x + 4

g of x is less than or equal to negative one half times x minus 5

Explanation:

From the above graph,

If point B is the solution of the system of inequalities, then point B must satisfies both inequalities

We can see from the graph that

Point B is located above (≥) the boundary line for f(x) and is also below (≤) the boundary line for g(x).

So we can say,

Point b satisfies the inequalities

Therefore,

The system is

f(x) ≥ (3x+4)

g(x) ≤ (-1/2x -5)

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