NJGPA Creating and Solving Equations and Inequalities 4

Question 1

Two friends start with different amounts of money. Aisha has $120 and spends $15 per week. Ben has $60 and spends $5 per week. After how many weeks will they have the same amount?

Accepted Answer

6

Answer

Set 120 − 15w = 60 − 5w; solving gives −10w = −60, so w = 6.

Question 2

Which equation has no solution?

Accepted Answer

2x + 3 = 2x − 1

Answer

2x + 3 = 2x − 1 simplifies to 3 = −1, which is a contradiction and has no solution.

Question 3

A farmer wants to fence a rectangular pen along a barn wall using 80 feet of fencing for 3 sides. If the width is w, what is the maximum area when the length is 80 − 2w?

Accepted Answer

w(80 − 2w)

Answer

Area = width × length = w(80 − 2w).

Question 4

Solve: 5 − 2(x + 3) = −7

Accepted Answer

x = 2

Answer

Expand to 5 − 2x − 6 = −7, then −2x − 1 = −7, so −2x = −6 and x = 2 (correct is index 1).

Question 5

The solution set of 3x − 1 ≥ 5 is best described as:

Accepted Answer

x ≥ 2

Answer

Add 1 to both sides: 3x ≥ 6, then divide by 3: x ≥ 2.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

NJGPA Creating and Solving Equations and Inequalities 4