Question

suppose the college requires a new scale score greater than or equal to 1500 to admit a student. to determine what old score values would be equivalent to the new score that would result in admission to this college, complete parts (a) and (b).
the new scale score ( y ) is defined as a function of the old scale score ( x ) by the equation ( y = 0.89x + 126.5127 ).
(a) write an inequality in terms of ( x ) to represent the problem.
( 0.89x + 126.5127 geq 1500 ) (type an inequality. do not simplify.)
solve the above inequality algebraically.
( x geq 1543 ) (type an inequality. round to the nearest whole number as needed.)
(b) solve the inequality from part (a) graphically to verify the result. which of the following graphs is useful to verify the result?
options: a, b, c, d (with corresponding graphs)

Explanation:

Step1: State the given inequality

$0.89x + 126.5127 \geq 1500$

Step2: Isolate the x-term

Subtract 126.5127 from both sides:
$0.89x \geq 1500 - 126.5127$
$0.89x \geq 1373.4873$

Step3: Solve for x

Divide both sides by 0.89:
$x \geq \frac{1373.4873}{0.89}$
$x \geq 1543.244157...$
Round to nearest whole number: $x \geq 1543$

Step4: Identify correct graph

The inequality $x \geq 1543$ is a vertical line at $x=1543$, shaded to the right. This matches graph B (vertical red line at the x-value, shaded right, with the line crossing the x-axis at the solution point).

Answer:

(a) $0.89x + 126.5127 \geq 1500$
(b) $x \geq 1543$; Correct graph: B.