Consider the following expressions:
6 - 1/4 times 28 - 2 1/4 ________ 3/4 + 2 times 2 - 11
Which operator cab be inserted to make the statement true?
The operator that can be inserted to make the statement true is the addition operator (+). The correct expression would be:
6 - 1/4 * 28 - 2 1/4 + 3/4 + 2 * 2 - 11
Consider the following expressions:
6 - 1/4 times 28 - 2 1/4 ________ 3/4 + 2 times 2 - 11
Which operator cab be inserted to make the statement true?
A. >_
B. =
C. <
D. >
To determine which operator can be inserted to make the statement true, let's simplify the given expression:
6 - 1/4 * 28 - 2 1/4 ________ 3/4 + 2 * 2 - 11
= 6 - 7 - 2 1/4 ________ 3/4 + 4 - 11
= -1 - 2 1/4 ________ 3/4 - 7
= -1 - (2 + 1/4) ________ (3 - 7/4)
= -1 - (9/4) ________ (12/4 - 7/4)
= -1 - (9/4) ________ 5/4
Now let's compare the two sides of the expression:
-1 - (9/4) _____ 5/4
To evaluate this comparison, we can convert both sides to have a common denominator:
-1 - (9/4) _____ 5/4
-4/4 - (9/4) _____ 5/4
(-4 - 9)/4 _____ 5/4
-13/4 _____ 5/4
Since -13/4 is less than 5/4, we can conclude that the correct operator to make the statement true is C. < (less than).
Which of the following values for b makes the inequality -32.5 - 6b >_ 48.5 true?
To find the values of b that make the inequality true, we can solve for b.
The inequality is: -32.5 - 6b ≥ 48.5
Let's start by isolating the variable b.
Add 32.5 to both sides of the inequality:
-32.5 - 32.5 - 6b ≥ 48.5 + 32.5
-6b ≥ 81
Divide both sides of the inequality by -6, remembering to reverse the inequality sign when dividing by a negative number:
b ≤ 81 / -6
Simplifying:
b ≤ -13.5
Therefore, any value of b that is less than or equal to -13.5 will make the inequality -32.5 - 6b ≥ 48.5 true.
Which of the following equations has the solution set {-3}?
A. 4x + 8 = -4
B. 4x + 8 = 4
C. 4x - 8 = 4
D. 4x - 8 = -4
To find which equation has the solution set {-3}, we can substitute -3 for x and see which equation holds true.
A. 4(-3) + 8 = -4
-12 + 8 = -4
-4 = -4 - This equation is false.
B. 4(-3) + 8 = 4
-12 + 8 = 4
-4 = 4 - This equation is false.
C. 4(-3) - 8 = 4
-12 - 8 = 4
-20 = 4 - This equation is false.
D. 4(-3) - 8 = -4
-12 - 8 = -4
-20 = -4 - This equation is true.
Therefore, the equation that has the solution set {-3} is D. 4x - 8 = -4.
Which set expresses the solution to the compound inequality -2 <_ 2x + 1/3 -4 <1?
A. { x : 5/2 <_ x < 7}
B. { x : 5/2 <_ x < 1}
C. { x : 3 <_ x <7}
D. { x : -3/2 <_ x <1}
To find the solution to the compound inequality -2 ≤ 2x + 1/3 - 4 < 1, we need to solve each individual inequality and then find the intersection of the solution sets.
First, let's solve the left inequality: -2 ≤ 2x + 1/3 - 4
Adding 4 to both sides:
2 ≤ 2x + 1/3
Subtracting 1/3 from both sides:
2 - 1/3 ≤ 2x
Multiplying both sides by 1/2:
1 2/3 ≤ x
So the solution to the left inequality is x ≥ 1 2/3 or x ≥ 5/3.
Now let's solve the right inequality: 2x + 1/3 - 4 < 1
Adding 4 to both sides:
2x + 1/3 - 4 + 4 < 1 + 4
2x + 1/3 < 5
Subtracting 1/3 from both sides:
2x < 5 - 1/3
Simplifying:
2x < 14/3
Dividing both sides by 2:
x < 7/3
So the solution to the right inequality is x < 7/3.
As we are looking for the intersection of both solution sets, the solution to the compound inequality is: x ≥ 5/3 and x < 7/3.
Simplifying this interval notation, we get:
{ x: 5/3 ≤ x < 7/3}
which is the same as:
{ x: 1 2/3 ≤ x < 2 1/3}
Therefore, the correct answer is A. { x: 5/2 ≤ x < 7}