The following inequality is solved for x.
Line A 4(x + 1) + 8 ≥ 4 + 2x
Line B 4x + 4 + 8 ≥ 4 + 2x
Line C 4x + 12 ≥ 4 + 2x
Line D 2x + 12 ≥ 4
Line E 2x ≥ - 8
Line F x ≥ -4
Which Line shows the inequality after you use the division property?
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1 point
Line B 4x + 4 + 8 ≥ 4 + 2x
Line C 4x + 12 ≥ 4 + 2x
Line D 2x + 12 ≥ 4
Line E 2x ≥ - 8
Line F x ≥ -4
The line that shows the inequality after using the division property is Line E: 2x ≥ -8.
Mari is solving the inequality 4(x - 3)+2 > 16. Her first step is 4x - 12 +2 > 16.
Which step should be the next step?
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1 point
4x-12 - 2 > 16 -2
4x-4x-12+2>16-4x
4x-10>16
4x > 26
The next step should be: 4x - 10 > 16.
Javon and Ivy are both given the equation 16≤-3-5n-1. Javon thinks the first step is 16≤-4-5n. Ivy thinks the first step is 16+1≤-3-5n-1+1. Who is incorrect and why?
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1 point
Ivy is incorrect because you should combine Like Terms before you move constants
Javon is incorrect because you should move each constant to the other side one at a time.
They are both correct because order does not matter if you get the same answer in the end.
Ivy is incorrect because you should combine like terms before moving constants. In this case, the 1 on the left side of the equation should be added to the 16, not to the -1. Therefore, the correct first step is 16 + 1 ≤ -3 - 5n + 1.
Consider the inequality -10+2x ≥ 8(-6 + 5x).
The solution set of the inequality is:
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1 point
x≥ -40
x≤ -40
x≤1
x≥1
The solution set of the inequality is x ≥ -40.
40 - 5k ≤ - 7(1 - 6k)
solve inequality for k
To solve the inequality for k, we can begin by simplifying both sides.
Starting with the left side of the inequality:
40 - 5k
Next, we can simplify the right side of the inequality:
- 7(1 - 6k)
= -7 + 42k
Now, the inequality becomes:
40 - 5k ≤ -7 + 42k
To isolate the terms with k, we can rearrange the inequality:
-5k - 42k ≤ -7 - 40
-47k ≤ -47
To solve for k, we need to isolate it by dividing both sides of the inequality by -47. However, since we are dividing by a negative number, the inequality sign will flip.
k ≥ (-47)/(-47)
k ≥ 1
So the solution to the inequality is k ≥ 1.