Answer: -1 < x < 8
x = 3
x ≠ 2
<u>Step-by-step explanation:</u>
Isolate x in the middle. Perform operations to all 3 sides.
-6 < 2x - 4 < 12
<u>+4 </u> <u> +4</u> <u>+4 </u>
-2 < 2x < 16
<u>÷2 </u> <u>÷2 </u> <u> ÷2 </u>
-1 < x < 8
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Isolate x. Solve each inequality separately. Remember to flip the sign when dividing by a negative.
4x ≤ 12 and -7x ≤ 21
<u>÷4 </u> <u>÷4 </u> <u> ÷-7 </u> <u>÷-7 </u>
x ≤ 3 and x ≥ 3
Since it is an "and" statement, x is the intersection of both inequalities.
When is x ≤ 3 and ≥ 3? <em>when x = 3</em>
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Isolate x. Solve each inequality separately.
15x > 30 or 18x < -36
<u>÷15 </u> <u> ÷15 </u> <u> ÷18 </u> <u>÷18 </u>
x > 2 or x < 2
Since it is an "or" statement, x is the union of both inequalities.
When we combine the inequalities, x is every value except 2.
x ≠ 2
Answer:
2nd option
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
- 3x - 2y = 30 ( add 3x to both sides )
- 2y = 3x + 30 ( divide terms by - 2 )
y = - 
x - 15 ← in slope- intercept form
2x^2 = 2
so x needs to equal 1 since 2*1 = 2
Answer:
4 feet.
Step-by-step explanation:
Let x be the height of tower when finished.
We have been given that Priya takes a break when the tower is 2 and 1/2 feet tall, which is 5/8 of the height of the tower she wants to build.
This means that 5/8 of x equals 
. Let us represent this information in an equation.
Let us convert our given mixed fraction into improper fraction.
Let us multiply both sides of our equation by 8/5.
Therefore, the tower will be 4 feet tall when finished.
Answer:
C. For each bolt the number of cracks decreased by an average of 1/2.
Step-by-step explanation:
Consider the points (2, 8) and (8, 5) on the line.
The number of cracks decreased from 8 to 5 while the number of bolts increased from 2 to 8. Thats a ratio of -3 : 6, which supports choice C.
