1. 5h – 9 = –16 + 6h
A) 4
B) –7
C) 7 <-------------------------
D) 10
2. 4x + 4 = 9x – 36
A) -8
B) –7
C) 8 <-------------------------
D) –3
3. Which of the following equations has an infinite number of solutions?
A) 3x – 3 = –4x
B) 2y + 4 – y = 16
C) 7x + 5 = 4x + 5 + 3x <-----------
D) 6y – 2 = 2(y – 1)
4. Write an inequality for the word sentence: k is less than zero.
A) k > 0
B) k ≥ 0
C) k < 0 <-------------------------
D) k ≤ 0
5. q – 12 ≥ –13
A) q ≥ 1 <-------------------------
B) q ≥ –1
C) q ≥ 25
D) q ≥ –25
6. 12p < 96
A) p < 8 <---------------------
B) p < 108
C) p < 84
D) p < –8
7. g/-5 < –18
A) g < –23 <---------------------
B) g > –90
C) g > 90
D) g < 90
8. The result of 6 subtracted from a number n is at least 2. What numbers are solutions?
A) n – 2 > 6; n > 8
B) n – 6 ≥ 2; n ≥ 8<----------------
C) n + 6 ≥ 2; n ≤ 4
D) n + 6 ≥ 2; n ≥ 4
All are good except #7
g/-5 < -18
to "clear" the -5, we multiply both sides by -5, thus reversing the inequality sign
g > +90 , which is C
(looks like you added the -5)
I got them right, except on #5 the answer is B.
To solve each of these problems, we will go through the steps and show the answers:
1. 5h - 9 = -16 + 6h
To solve for h, let's first simplify the equation by combining like terms:
Subtract 6h from both sides: 5h - 6h - 9 = -16
Simplify: -h - 9 = -16
Now, add 9 to both sides: -h - 9 + 9 = -16 + 9
Simplify: -h = -7
To isolate h, multiply both sides by -1 (to flip the sign): -1*(-h) = -1*(-7)
Simplify: h = 7
So, the answer is C) 7.
2. 4x + 4 = 9x - 36
To solve for x, we will again simplify the equation by combining like terms:
Subtract 4x from both sides: 4x - 4x + 4 = 9x - 4x - 36
Simplify: 4 = 5x - 36
Now, add 36 to both sides: 4 + 36 = 5x - 36 + 36
Simplify: 40 = 5x
To isolate x, divide both sides by 5: 40/5 = 5x/5
Simplify: 8 = x
So, the answer is C) 8.
3. Which of the following equations has an infinite number of solutions?
An equation has an infinite number of solutions if its terms can be simplified to something like 0 = 0, where both sides are equal.
Looking at the options:
A) 3x - 3 = -4x
Let's simplify: 7x - 3 = 0
This equation does not have an infinite number of solutions.
B) 2y + 4 - y = 16
Simplifying, we get: y + 4 = 16
This equation does not have an infinite number of solutions.
C) 7x + 5 = 4x + 5 + 3x
Simplifying, we get: 7x + 5 = 7x + 5
This equation has an infinite number of solutions.
So, the answer is C) 7x + 5 = 4x + 5 + 3x.
4. Write an inequality for the word sentence: k is less than zero.
If k is less than zero, we can represent it using the less than symbol (<).
So, the answer is C) k < 0.
5. q - 12 ≥ -13
To solve for q, we will simplify the inequality by adding 12 to both sides: q - 12 + 12 ≥ -13 + 12
Simplify: q ≥ -1
So, the answer is A) q ≥ -1.
6. 12p < 96
To solve for p, we will divide both sides by 12 to isolate p: (12p)/12 < 96/12
Simplify: p < 8
So, the answer is A) p < 8.
7. g/-5 < -18
To solve for g, we will multiply both sides by -5 (and flip the inequality sign since we are multiplying by a negative number): -5*(g/-5) > -18*(-5)
Simplify: g > 90
So, the answer is B) g > -90.
8. The result of 6 subtracted from a number n is at least 2. What numbers are solutions?
To solve for n, we will write the inequality for the given statement: n - 6 ≥ 2
So, the answer is B) n - 6 ≥ 2; n ≥ 8.