1)write an inequality
a. the sum of three times a number and 2 lies between 7 and 14
b.seven less than 4 times a number is at most 44 and at least -24.
2)which is not a solution of -4 is less than or equal to 2-6x less than or equal to 8.
3) 2x-1<x+2<6x+12
a. 0
b. 1
c. 2
d.-1
1a. 7 < (3x+2)<14.
2. -4<= 2-6x <= 8.
-4-2 <= -6x <= 8-2
-6 <= -6x <= 6
1 >= X >= -1
-1<= X <= 1.
S0 X can be any value from -1 to positive 1.
C. 2 is False. Not a solution.
3. 2x-1<x+2 < 6x+12
Solve the compound inequality as 2 separate inequalities.
2x-1 < x+2.
2x-x < 2+1
X < 3.
x+2 < 6x+12
x-6x < 12-2
-5x < 12-2
-5x < 10
X > -2.
Solution set: -2 < X < 3.
All values of X between -2 and 3 satisfies the compound inequality and
each single inequality.
1a) 7 < 3x + 2 < 14
1b) -24 ≤ 4x - 7 ≤ 44
2) A cow dancing on the moon while drinking pineapple juice from a coconut.
3) B. 1
1)
a. To write the inequality, let's let the number be represented by the variable "x":
The sum of three times the number and 2 can be written as: 3x + 2.
The inequality can be described as follows:
7 < 3x + 2 < 14
b. Let the number be represented by the variable "x" again:
Four times the number can be written as: 4x.
Seven less than four times the number can be written as: 4x - 7.
The inequality can be described as follows:
-24 ≤ 4x - 7 ≤ 44.
2)
To determine which value is not a solution, we need to find the value(s) of "x" that makes the inequality -4 ≤ 2 - 6x ≤ 8 true.
Let's solve each part of the inequality separately:
-4 ≤ 2 - 6x
-6x ≤ 2 + 4
-6x ≤ 6
x ≥ -1
2 - 6x ≤ 8
-6x ≤ 8 - 2
-6x ≤ 6
x ≥ -1
The values of "x" that make the inequality true are x ≥ -1.
Therefore, any value of "x" greater than or equal to -1 is a solution. To find the value that is not a solution, we need to find a value less than -1. For example, if we choose x = -2:
-4 ≤ 2 - 6(-2) ≤ 8
-4 ≤ 14 ≤ 8
This is not true, so x = -2 is not a solution.
3)
To solve the inequality 2x - 1 < x + 2 < 6x + 12, we need to isolate the variable "x" in the middle of the inequality.
2x - 1 < x + 2 < 6x + 12
First, let's solve for the left inequality:
2x - 1 < x + 2
2x - x < 2 + 1
x < 3
Now, let's solve for the right inequality:
x + 2 < 6x + 12
-5x < 10
x > -2
Putting it together, the solution is:
-2 < x < 3
Therefore, the correct answer is option c) 2.
1a) To write an inequality for "the sum of three times a number and 2 lies between 7 and 14," we can use the following steps:
Let's start by picking a variable to represent the number. Let's use "x" for this example.
We know that "the sum of three times a number and 2" can be represented by the expression 3x + 2.
The inequality can then be written as:
7 ≤ 3x + 2 ≤ 14
This inequality states that the value of 3x + 2 is between 7 and 14, inclusive.
1b) To write an inequality for "seven less than 4 times a number is at most 44 and at least -24," we can follow these steps:
Again, let's use the variable "x" to represent the number.
We know that "four times a number" can be represented by the expression 4x.
"The sum of seven less than four times a number" becomes 4x - 7.
The inequality can be written as:
-24 ≤ 4x - 7 ≤ 44
This inequality states that the value of 4x - 7 is between -24 and 44, inclusive.
2) To determine which value is not a solution of -4 ≤ 2 - 6x ≤ 8, we can follow these steps:
We have the compound inequality -4 ≤ 2 - 6x ≤ 8.
First, we solve the left inequality:
-4 ≤ 2 - 6x
Subtract 2 from both sides:
-6 ≤ -6x
Divide both sides by -6 (and remember that dividing by a negative number reverses the inequality):
1 ≥ x
Next, we solve the right inequality:
2 - 6x ≤ 8
Subtract 2 from both sides:
-6x ≤ 6
Divide by -6 (and reverse the inequality):
x ≥ -1
Combining the results, we have:
-1 ≤ x ≤ 1
To check if a value is not a solution, substitute it into the inequality and see if it holds true.
So, we substitute each value into the inequality:
For x = 0, we have -4 ≤ 2 - 6(0) ≤ 8, which is true.
For x = 1, we have -4 ≤ 2 - 6(1) ≤ 8, which is true.
Since both values satisfy the inequality, none of the given options (0, 1, 2, -1) are not a solution.
3) To determine which value satisfies the inequality 2x - 1 < x + 2 < 6x + 12, we can follow these steps:
Start by simplifying each inequality separately:
2x - 1 < x + 2
-1 < x + 2 - 2x
-1 < -x + 2
-1 - 2 < -x
-3 < -x
3 > x
x + 2 < 6x + 12
2 - 12 < 6x - x
-10 < 5x
-2 > x
Combining the results, we have:
-2 > x > 3
Checking the given options:
a. 0: -2 > 0 > 3 (not true)
b. 1: -2 > 1 > 3 (not true)
c. 2: -2 > 2 > 3 (not true)
d. -1: -2 > -1 > 3 (true)
Hence, the only value that satisfies the inequality is d. -1.