Answer:
C, E, and F
Explanation:
There are two ways to answer this question. First, you could simply input each answer into both equations to see which one works but that would take quite a long time.
A better way is to simply solve each equation for x.
You could rewrite
2x + 7 < -3
as
2x + 7 = -3
and solve:
Subtract 7 from both sides
![(2x + 7) -7 = (-3) - 7\\2x = -10](https://tex.z-dn.net/?f=%282x%20%2B%207%29%20-7%20%3D%20%28-3%29%20-%207%5C%5C2x%20%3D%20-10)
Now divide both sides by 2
![\frac{2x}{2} = \frac{-10}{2}\\x = -5](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%20%20%3D%20%5Cfrac%7B-10%7D%7B2%7D%5C%5Cx%20%3D%20-5)
Now we can simply replace the equals sign with the inequality
x < -5
Where you can run into trouble is if you have to multiply or divide by a negative number across the equation, you must flip the inequality sign. It's best to leave it there to remind you, but I switched it out just to show that it's no different than a typical algebraic equation.
Now, we know that x can be any value less than -5. Let's find out the same thing for the second equation:
![x - 8 + 3x < -4\\(x + 3x) -8 < -4\\4x - 8 < -4\\(4x - 8) + 8 < (-4) + 8\\4x < 4\\\frac{4x}{4} < \frac{4}{4}\\x < 1](https://tex.z-dn.net/?f=x%20-%208%20%2B%203x%20%3C%20-4%5C%5C%28x%20%2B%203x%29%20-8%20%3C%20-4%5C%5C4x%20-%208%20%3C%20-4%5C%5C%284x%20-%208%29%20%2B%208%20%3C%20%28-4%29%20%2B%208%5C%5C4x%20%3C%204%5C%5C%5Cfrac%7B4x%7D%7B4%7D%20%3C%20%5Cfrac%7B4%7D%7B4%7D%5C%5Cx%20%3C%201)
Now we know that x must be less than 1 for the second equation. So, now we can choose the answers that are both less than -5 and less than 1.
These answers are:
C. -10
E. -8.24
and
F. -15/2 which is -7.5
NOTE: -5 is equal to but not less than -5 so G is not included.
Answer:
1)
1. Given
2. Vertical Angles Theorem
3. SAS Congruence Postulate
2)
1. Given
2. Definition of Angle Bisector
3. Definition of Perpendicular Lines
4. All right angles are congruent.
5. Reflexive Property
6. ASA Congruence Postulate
3)
1. AC is the perpendicular bisector of PT.
2. Definition of Bisector
3. AC = AC
4. Definition of Perpendicular Bisector
5. <PCA = <TCA
6. SAS Congruence Postulate.
7. PA = TA; CPCTC
Step-by-step explanation:
None necessary.
Word form: sixty-seven-thousand eleven.
Expanded form: 60,000 + 7,000 + 11
B. Discount because when taking a percentage of the price off you are discounting the item
Since top 3 racers recognized with the same award, answer is 3/12 or 1/4 or .25