Pls answer I need it quick
1. If ƒ(x) = 4x – 11, what is the value of ƒ(5)?
A. 20x – 55
B. 34
C. 9....
D. 4
2. If the length (L) of a rectangle is 3 less than 4 times the width (W) of the rectangle, which of the following equations represents the relationship between the length and the width of the rectangle?
A. L = 3 – 4W.....
B. L = 4W – 3
C. W = 3 – 4L
D. W = 4L – 3
4. Sam wants to paint his living room and he needs to buy some materials. Cans of paint cost $10 each and paint brushes each cost $2 each. If Sam plans to spend exactly $50 on painting materials, which of the following equations represents the number of cans of paint (c) and the number of paint brushes (b) that he can purchase?
A. $10c + $2b = $50
B. $10b + $2c = $50
C. $12(c + b) = $50
D. $2(5c × b) = $50....
5. Solve:
(4x + 6) = 5
2(3r + 4) – 3(r + 1) = 11
A. r = 0
B. r = 2
C. r = 3 ....
D. r = 6
6. Solve for x: 3(x – 2) = 9
A. –5
B. –4
C. 4
D. 5....
7. Which answer BEST describes the solution for x if –3 < x + 4 ≤ 7?
A. x > –7...
B. x > –7 and x < 3
C. x ≥ –7 and x ≤ 3
D. x > –7 and x ≤ 3
8. Solve the compound inequality: 2x – 4 < –8 or x + 2 > 5
A. x < –2
B. x > –2 or x < 3
C. x < –2 or x > 3....
D. x > 3
9. What is the solution to the inequality –2x + 8 < 3(2x – 4)?
A. x < 1
B. x > –1....
C. x< 5/2
D. x> 5/2
1. Correct.
2. Width = W.
Length = 4W - 3.
L = 4W - 3.
4. $10c + $2b = $50.
5. 4x + 6 = 5, 4x = 5 - 6, X = -1/4.
2(3r + 4) - 3(r + 1) = 11.
6r + 8 - 3r - 3 = 11,
r = ?
6. Correct.
9. -2x + 8 < 3(2x - 4).
-2x + 8 < 6x - 12,
-2x-6x < -20,
-8x < -20,
X > 20/8,
X > 5/2.
Note: When dividing or multiplying by a neg. number, the inequality sign is reversed.
1 yes
2 no
4 no but where is 3 maybe x=-1/4
5 no
6 yes
7 c
8 yes
9 no.... >5/2
because
-2x + 8 < 6 x - 12
-8 x <-20
when change sign, reverse arrow
8 x > 20
x > 20/8 or 5/2
8
Sure! Here are the explanations for each question:
1. If ƒ(x) = 4x – 11, to find the value of ƒ(5), you simply substitute x=5 into the equation. So, ƒ(5) = 4(5) - 11 = 20 - 11 = 9. Therefore, the answer is C. 9.
2. The problem states that the length of the rectangle (L) is 3 less than 4 times the width (W). This can be represented as L = 4W - 3. So, the answer is B. L = 4W - 3.
3. In this problem, the cost of paint cans is $10 each and paint brushes cost $2 each. The total budget is $50. So, the equation that represents this situation is $10c + $2b = $50, where c represents the number of cans of paint and b represents the number of paint brushes. Therefore, the answer is A. $10c + $2b = $50.
4. To solve the equation (4x + 6) = 5, you need to isolate the variable x. Start by subtracting 6 from both sides of the equation: 4x = 5 - 6 = -1. Then divide both sides by 4 to get x = -1/4. So, the answer is none of the listed options.
5. To solve the equation 3(x - 2) = 9, you need to isolate the variable x. Start by distributing the 3 on the left side of the equation: 3x - 6 = 9. Then add 6 to both sides of the equation: 3x = 9 + 6 = 15. Finally, divide both sides by 3 to get x = 15/3 = 5. So, the answer is D. 5.
6. The given inequality is -3 < x + 4 ≤ 7. To find the solution, you need to rewrite it as separate inequalities. From the given inequality, subtract 4 from all sides to get -7 < x ≤ 3. Therefore, the answer is D. x > -7 and x ≤ 3.
7. To solve the compound inequality 2x - 4 < -8 or x + 2 > 5, you need to solve each inequality separately and then find the solution that satisfies both inequalities. For the first inequality, add 4 to both sides to get 2x < -4. Then divide both sides by 2 to get x < -2. For the second inequality, subtract 2 from both sides to get x > 3. Therefore, the answer is C. x < -2 or x > 3.
8. The inequality -2x + 8 < 3(2x - 4) can be simplified by distributing 3 on the right side of the inequality: -2x + 8 < 6x - 12. Combine like terms by adding 2x to both sides to get 8 < 8x - 12. Then add 12 to both sides to get 20 < 8x. Finally, divide both sides by 8 to get x > 20/8 = 5/2. Therefore, the answer is D. x > 5/2.
I hope this helps you understand how to solve each problem! Let me know if you have any further questions.