Let's solve the first inequality at first. So,
−2(x + 4) + 10 < x − 7
-2x- 8 + 10 < x - 7 By distribution property.
-2x + 2 < x - 7 Adding the like terms.
-2x < x - 7 - 2 Subtract 2 from each sides.
-2x < x - 9 By simplifying.
-2x - x < -9 Subtract x from each sides.
-3x < -9
Since we are dividing by negative 3. So, sign of inequality will get change.
So, x>3
Now the next inequality is,
−2x + 9 > 3(x + 8)
-2x + 9 > 3x + 24
-2x > 3x + 24 - 9
-2x > 3x + 15
-2x - 3x > 15
-5x >15
So, x <-3
Hence, the correct choice is x > 3 or x < −3.
The answer choices would be: A, D, and E. These would be the correct answer choices because commutative property only works for addition and multiplication. Therefore, C and F are incorrect. B would also be incorrect because it is showing the Distributive Property. I hope this helps!
Answer:
Question 18
=$3.33
Step-by-step explanation:
i)
26/100 x 4.5
=1.17
(the discount price)
ii)
$4.5-$1.17
=$3.33
<span>The diagonals are congruent.
</span>
To solve this problem you must apply the proccedure shown below:
1- If the triangle is a rigth triangle, you must apply the Pythagorean Theorem. Taking the length 3 inches as the hypotenuse, which is the longest side of the triangle, you have:
a^2=b^2+c^2
c=√(a^2-b^2)
b=3/4 inches
a=3 inches
2- When you susbtitute the values, you obtain:
c=√(3 inches)^2-(3/4 inches)^2
c=2.90 inches
The answer is: 2.90 inches.
