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:
The numerator is the first number in a division problem (dividend). The denominator is the second number in a division problem (divisor).
Answer:
ED = 8 units
Step-by-step explanation:
ΔAEB and ΔDEC are similar triangles, hence the ratios of corresponding sides are equal, that is
=
, that is
=
( cross- multiply )
6(2x + 4) = 9(x + 4) ← distribute parenthesis on both sides
12x + 24 = 9x + 36 ( subtract 9x from both sides )
3x + 24 = 36 ( subtract 24 from both sides )
3x = 12 ( divide both sides by 3 )
x = 4
Hence ED = x + 4 = 4 + 4 = 8 units
Answer:
D. 0.65
Step-by-step explanation:
0.05 x 5=0.25
0.01 x 5=0.05
0.07 x 5=0.35
0.25+0.05+0.35=0.65
the all must pay 0.65 each