Math Knowledge ASVAB Test 2024 With Complete Solutions

A: First, the distributive property must be used on the left side. This results in 3x + 6 = 14x -5. The addition property is then used to add 5 to both sides, and then to subtract 3x from both sides, resulting in 11 = 11x. Finally, the multiplication property is used to divide each side by 11. Therefore, x = 1 is the solution. - What is the solution? D: First, like terms are collected to obtain 12 - 5x = -5x + 12. Then, the addition principle is used to move the terms with the variable, so 5x is added to both sides and the mathematical statement 12 = 12 is obtained. This is always true; therefore, all real numbers satisfy the original equation. - What is the solution? E: The distributive property is used on both sides to obtain 4x + 20 + 6 = 4x + 6. Then, like terms are collected on the left, resulting in 4x + 26 = 4x + 6. Next, the addition principle is used to subtract 4x from both sides, and this results in the false statement 26 = 6. Therefore, there is no solution. - What is the solution? D: This is a one-step real-world application problem. The unknown quantity is the number of cases of cola to be purchased. Let be equal to this amount. Because each case costs $3.50, the total number of cases times $3.50 must equal $40. This translates to the mathematical equation 3.5x = 40 Divide both sides by 3.5 to obtain x = 11.4286, which has been rounded to four decimal places. Because cases are sold whole (the store does not sell portions of cases), and there is not enough money to purchase 12 cases, there is only enough money to purchase 11. - 4. How many cases of cola can Lexi purchase if each case is $3.50 and she has $40? a. 10