Welcome to our “Daily Math Practice Challenge: Preparing for the ACT Exam”! This challenge is designed to help you engage in targeted math practice every day, gearing up for the ACT exam. Through daily exercises, you will enhance your problem-solving speed, deepen your understanding of mathematical concepts, and strengthen your ability to tackle a variety of math problems.
1. Given 3x − 7 = 8x − 16 is true, x = ?
2. As shown in the figure below, points A, B, and D lie on a line. The measure of angle ABC (m∠ABC) is x°, and m∠CBD is (5x + 4)°.
Which of the following equations is true?
A. (5x + 4) = x
B. x − (5x + 4) = 90
C. x + (5x + 4) = 90
D. x + (5x + 4) = 180
E. x + (5x + 4) = 360
3. A restaurant currently has an outdoor rectangular dining section measuring 30 feet by 40 feet. The shorter sides will be increased by 10 feet each, resulting in a larger rectangular dining section. What is the positive difference, in square feet, between the areas of the resulting and current dining sections?
F. 100
G. 300
H. 400
J. 500
K. 600
4. What is the value of ⎪−4⎪ − ⎪6 − 29⎪ ?
A. −31
B. −27
C. −19
D. 19
E. 27
5. Christopher works in a clothing store. He earns $7.50 per hour, plus 6% of his sales. Which of the following expressions gives Christopher’s earnings, in dollars, when he works x hours and has y dollars in sales?
F. 75x + 6y
G. 75x + 0.06y
H. 7.5x + 6y
J. 7.5x + 0.6y
K. 7.5x + 0.06y