This is on Lesson 9 Unit 7 Equations and Inequalties Unit Test
6: -6 - 7(c + 10)
answer: 4 - 13c
7: 3x + 4(x - 6) - 3(x - 7)
no answer
9: d/13 ≤ -3
no answer
14: Mark weighs 74 pounds. Together, he and his sister weigh six pounds more than three times the weight of his sister. What is the weight, w, or Mark's sister?
answer: 35 lb.
i neeD hElp sO bAd plEasE aND thAnk yOU
what are the answers to this whole test?
Of course, I'm here to help! Let's go through each question step by step.
Question 6: -6 - 7(c + 10)
To simplify this equation, we need to distribute the -7 to both terms inside the parenthesis:
-6 - 7c - 7(10)
Next, simplify the multiplication: -7 * 10 = -70
-6 - 7c - 70
Combine the like terms: -6 and -70
-76 - 7c
So, the simplified form of the equation is -76 - 7c or 4 - 13c.
Question 7: 3x + 4(x - 6) - 3(x - 7)
To simplify this equation, we need to distribute the 4 and -3 to the terms inside the parentheses:
3x + 4x - 24 - 3x + 21
Combine the like terms:
3x + 4x - 3x + 21 - 24
Simplify the addition and subtraction:
4x - 3
So, the simplified form of the equation is 4x - 3.
Question 9: d/13 ≤ -3
To solve this inequality, we can multiply both sides of the inequality by 13 to get rid of the denominator:
13 * (d/13) ≤ -3 * 13
Simplifying:
d ≤ -39
So, the solution to the inequality is d ≤ -39.
Question 14: Mark weighs 74 pounds. Together, he and his sister weigh six pounds more than three times the weight of his sister. What is the weight, w, of Mark's sister?
Let's represent the weight of Mark's sister as w. We are given that Mark weighs 74 pounds and together they weigh six pounds more than three times the weight of his sister. Mathematically, we can write this as:
74 + w = 3w + 6
To solve for w, let's isolate the variable on one side:
74 + w - 3w = 6
Combine like terms:
74 - 2w = 6
Now, let's isolate the variable on one side by subtracting 74 from both sides of the equation:
74 - 2w - 74 = 6 - 74
Simplifying:
-2w = -68
To solve for w, we can divide both sides of the equation by -2:
-2w / -2 = -68 / -2
Simplifying:
w = 34
So, the weight of Mark's sister, w, is 34 pounds.
Of course, I'm here to help! Let's go through each question step by step.
6: -6 - 7(c + 10)
To simplify this expression, we need to distribute the -7 to both terms inside the parentheses:
-6 - 7c - 70
Combine like terms:
-7c - 76
So the simplified form of the expression -6 - 7(c + 10) is -7c - 76.
7: 3x + 4(x - 6) - 3(x - 7)
Again, let's start by distributing the terms inside the parentheses:
3x + 4x - 24 - 3x + 21
Combine like terms:
4x - 3x + 3x - 24 + 21
Combining further, we get:
4x - 24 + 21
4x - 3
So the simplified form of 3x + 4(x - 6) - 3(x - 7) is 4x - 3.
9: d/13 ≤ -3
To solve this inequality, we'll multiply both sides of the inequality by 13:
(d/13) * 13 ≤ (-3) * 13
This cancels out the 13 on the left-hand side:
d ≤ -39
So the solution to the inequality d/13 ≤ -3 is d ≤ -39.
14: Mark weighs 74 pounds. Together, he and his sister weigh six pounds more than three times the weight of his sister.
Let w represent the weight of Mark's sister. According to the problem, Mark and his sister together weigh six pounds more than three times the weight of his sister:
74 + w = 3w + 6
Rearranging the equation to isolate w:
w - 3w = 6 - 74
-2w = -68
Dividing both sides by -2:
w = 34
So the weight, w, of Mark's sister is 34 pounds.
I hope that helps! Let me know if you have any more questions or need further assistance.
#6: -6 - 7(c + 10)
= -6 -7c -70
= -7c-76
work #7 the same way
#9: d/13 ≤ -3
d ≤ -39
#10:
74+x = 6+3x
68 = 2x
x = 34