To solve the inequality, we need to isolate the variable x by subtracting 32 from both sides:
7x + 32 < 67
7x < 67 - 32
7x < 35
Next, divide both sides by 7 to solve for x:
x < 35/7
x < 5
The solution to the inequality is x < 5.
To graph this solution on the number line, we can draw a closed circle at 5 (since it is not included in the solution) and shade all the values to the left of 5.
Solve the inequality and graph the solution on the line provided.
7x+32<67
15 answers
Solve the inequality and graph the solution on the line provided.
5x−15<10
5x−15<10
To solve the inequality, we need to isolate the variable x by adding 15 to both sides:
5x - 15 < 10
5x < 25
Next, divide both sides by 5 to solve for x:
x < 25/5
x < 5
The solution to the inequality is x < 5.
To graph this solution on the number line, we can draw an open circle at 5 (since it is not included in the solution) and shade all the values to the left of 5.
5x - 15 < 10
5x < 25
Next, divide both sides by 5 to solve for x:
x < 25/5
x < 5
The solution to the inequality is x < 5.
To graph this solution on the number line, we can draw an open circle at 5 (since it is not included in the solution) and shade all the values to the left of 5.
Solve for xx and graph the solution on the number line below.
−1<x/-4
−1<x/-4
To solve the inequality, we need to multiply both sides by -4 to isolate x:
-4(-1) < x
Simplifying the equation, we get:
4 < x
So, the solution is x > 4.
To graph this solution on the number line, we can draw an open circle at 4 (since it is not included in the solution) and shade all the values to the right of 4.
-4(-1) < x
Simplifying the equation, we get:
4 < x
So, the solution is x > 4.
To graph this solution on the number line, we can draw an open circle at 4 (since it is not included in the solution) and shade all the values to the right of 4.
Solve for xx and graph the solution on the number line below
4x≥ −32
4x≥ −32
To solve the inequality, we need to divide both sides by 4:
4x/4 ≥ -32/4
x ≥ -8
So, the solution is x ≥ -8.
To graph this solution on the number line, we can draw a closed circle at -8 (since it is included in the solution) and shade all the values to the right of -8.
4x/4 ≥ -32/4
x ≥ -8
So, the solution is x ≥ -8.
To graph this solution on the number line, we can draw a closed circle at -8 (since it is included in the solution) and shade all the values to the right of -8.
Solve for xx and graph the solution on the number line below.
−4>x−9
−4>x−9
To solve the inequality, we will isolate x by adding 9 to both sides:
-4 > x - 9
This can be re-arranged as:
x - 9 < -4
Next, we will add 9 to both sides:
x < 5
So, the solution is x < 5.
To graph this solution on the number line, we can draw an open circle at 5 (since it is not included in the solution) and shade all the values to the left of 5.
-4 > x - 9
This can be re-arranged as:
x - 9 < -4
Next, we will add 9 to both sides:
x < 5
So, the solution is x < 5.
To graph this solution on the number line, we can draw an open circle at 5 (since it is not included in the solution) and shade all the values to the left of 5.
Solve for x and graph the solution on the number line below.
x+8<14
x+8<14
To solve the inequality, we will isolate x by subtracting 8 from both sides:
x + 8 - 8 < 14 - 8
This simplifies to:
x < 6
So, the solution is x < 6.
To graph this solution on the number line, we can draw an open circle at 6 (since it is not included in the solution) and shade all the values to the left of 6.
x + 8 - 8 < 14 - 8
This simplifies to:
x < 6
So, the solution is x < 6.
To graph this solution on the number line, we can draw an open circle at 6 (since it is not included in the solution) and shade all the values to the left of 6.
Select the values that make the inequality minus, 2, a, is greater than, 44−2a>44 true. Then write an equivalent inequality, in terms of aa.
(Numbers written in order from least to greatest going across.)
-32 -27 -25
-23 -22 -21
-19 -17 -12
(Numbers written in order from least to greatest going across.)
-32 -27 -25
-23 -22 -21
-19 -17 -12
To determine which values make the inequality true, we substitute each value into the inequality and check if it holds true.
For -32:
44 - 2(-32) > 44
44 + 64 > 44
108 > 44
Since 108 is indeed greater than 44, -32 satisfies the inequality.
For -27:
44 - 2(-27) > 44
44 + 54 > 44
98 > 44
Similarly, 98 is greater than 44, so -27 also satisfies the inequality.
For -25:
44 - 2(-25) > 44
44 + 50 > 44
94 > 44
Once again, 94 is greater than 44, so -25 satisfies the inequality.
For -23:
44 - 2(-23) > 44
44 + 46 > 44
90 > 44
Again, 90 is greater than 44, so -23 satisfies the inequality.
For -22:
44 - 2(-22) > 44
44 + 44 > 44
88 > 44
Once more, 88 is greater than 44, so -22 satisfies the inequality.
For -21:
44 - 2(-21) > 44
44 + 42 > 44
86 > 44
As before, 86 is greater than 44, so -21 satisfies the inequality.
For -19:
44 - 2(-19) > 44
44 + 38 > 44
82 > 44
82 is greater than 44, so -19 satisfies the inequality.
For -17:
44 - 2(-17) > 44
44 + 34 > 44
78 > 44
Once more, 78 is greater than 44, so -17 satisfies the inequality.
For -12:
44 - 2(-12) > 44
44 + 24 > 44
68 > 44
Finally, 68 is greater than 44, so -12 satisfies the inequality.
In summary, all the given values (-32, -27, -25, -23, -22, -21, -19, -17, -12) make the inequality 44 - 2a > 44 true.
To write an equivalent inequality in terms of a, we can distribute the -2 to get:
-2a + 44 > 44
Simplifying further, we have:
-2a > 0
Then, dividing both sides of the inequality by -2 and reversing the inequality symbol due to division by a negative number, we get:
a < 0
Therefore, an equivalent inequality in terms of a is a < 0.
For -32:
44 - 2(-32) > 44
44 + 64 > 44
108 > 44
Since 108 is indeed greater than 44, -32 satisfies the inequality.
For -27:
44 - 2(-27) > 44
44 + 54 > 44
98 > 44
Similarly, 98 is greater than 44, so -27 also satisfies the inequality.
For -25:
44 - 2(-25) > 44
44 + 50 > 44
94 > 44
Once again, 94 is greater than 44, so -25 satisfies the inequality.
For -23:
44 - 2(-23) > 44
44 + 46 > 44
90 > 44
Again, 90 is greater than 44, so -23 satisfies the inequality.
For -22:
44 - 2(-22) > 44
44 + 44 > 44
88 > 44
Once more, 88 is greater than 44, so -22 satisfies the inequality.
For -21:
44 - 2(-21) > 44
44 + 42 > 44
86 > 44
As before, 86 is greater than 44, so -21 satisfies the inequality.
For -19:
44 - 2(-19) > 44
44 + 38 > 44
82 > 44
82 is greater than 44, so -19 satisfies the inequality.
For -17:
44 - 2(-17) > 44
44 + 34 > 44
78 > 44
Once more, 78 is greater than 44, so -17 satisfies the inequality.
For -12:
44 - 2(-12) > 44
44 + 24 > 44
68 > 44
Finally, 68 is greater than 44, so -12 satisfies the inequality.
In summary, all the given values (-32, -27, -25, -23, -22, -21, -19, -17, -12) make the inequality 44 - 2a > 44 true.
To write an equivalent inequality in terms of a, we can distribute the -2 to get:
-2a + 44 > 44
Simplifying further, we have:
-2a > 0
Then, dividing both sides of the inequality by -2 and reversing the inequality symbol due to division by a negative number, we get:
a < 0
Therefore, an equivalent inequality in terms of a is a < 0.
which values do i pick to use in my answer?
To determine which values to pick for your answer, you should choose the values that satisfy the original inequality, which is 44 - 2a > 44.
From the given options (-32, -27, -25, -23, -22, -21, -19, -17, -12), you should select the values that, when substituted into the inequality, make it true.
In this case, all of the given values (-32, -27, -25, -23, -22, -21, -19, -17, -12) satisfy the inequality and make it true. Therefore, you can use any of these values in your answer.
From the given options (-32, -27, -25, -23, -22, -21, -19, -17, -12), you should select the values that, when substituted into the inequality, make it true.
In this case, all of the given values (-32, -27, -25, -23, -22, -21, -19, -17, -12) satisfy the inequality and make it true. Therefore, you can use any of these values in your answer.
1 answer