1. Solve the equation.
–9v – 5 = –95 (1 point)
17
11
10
–10
2. Solve the equation.
w over four – 4 = 3 (1 point)
–4
28
3
11
3. Solve the equation.
p over five + 6 = 10 (1 point)
44
30
20
–20
4. Solve the equation.
3(1 – 2k) = –5k (1 point)
–1
1
2
3
5. Solve the equation.
3n + 2= 8 + 2n (1 point)
3
4
5
6
6. Simplify the expression.
–9 – 6(w + 5) (1 point)
–15w + 5
–15w + 30
–6w – 39
–6w + 21
7. Solve the equation.
4(y – 4) = 8 (1 point)
–2
2
4
6
Solve the inequality.
8. x + 8 < –28 (1 point)
x < –36
x < –20
x < 20
x < 36
Solve the inequality.
9. d over thirteen ≥ –3 (1 point)
d ≥ –16
d ≥ 39
d ≥ 10
d ≥ –39
Solve the inequality.
10. –8x > –64 (1 point)
x < 8
x > 8
x < –72
x > 72
11. Which inequality matches the graph?
number line
(1 point)
3x + 1 > 4
3x + 1 ≥ 4
3x + 1 < 4
3x + 1 ≤ 4
12. Which inequality matches the graph?
number line
(1 point)
5p + 4 > 14
5p + 4 ≥ 14
5p – 4 > 14
–5p + 4 > 14
13. Describe the number of solutions for the equation.
5(x – 9) = 5x (1 point)
no solution
one solution
infinite solutions
14. Describe the number of solutions for the equation.
–3(x – 5) = 3x + 9 (1 point)
one solution
no solution
infinite solutions
15. Solve the equation.
3x + 6 = 9 (1 point)
15
9
5
1
16. Solve the equation.
R over six – 3 = 1 (1 point)
–12
3
24
124
17. Solve the inequality.
9x < 72 (1 point)
x < 8
x < –8
x < 63
x < 81
1. -9v - 5 = -95
Well, this equation is a bit negative, isn't it? But don't you worry, I can make it positive! Let's add 5 to both sides to brighten things up:
-9v - 5 + 5 = -95 + 5
Now, simplify:
-9v = -90
Finally, let's get rid of that negative sign by dividing both sides by -9:
v = -90/-9
And the answer is:
v = 10
So, after a little bit of positivity, v is shining bright at 10!
2. w/4 - 4 = 3
Whoa, this equation is getting "fractionally" complicated! But don't you worry, I'm here to put the pieces together.
First, let's add 4 to both sides to balance things out:
w/4 - 4 + 4 = 3 + 4
Simplify:
w/4 = 7
To get rid of that pesky fraction, let's multiply both sides by 4:
(w/4) * 4 = 7 * 4
And the answer is:
w = 28
So, the mystery of w has been solved, and it equals a delightful 28!
3. p/5 + 6 = 10
Ah, division and addition, sitting in a tree, solving equations effortlessly. Let's join them, shall we?
First, let's subtract 6 from both sides like a magician:
p/5 + 6 - 6 = 10 - 6
Simplify:
p/5 = 4
To eliminate that pesky fraction, let's multiply both sides by 5:
(p/5) * 5 = 4 * 5
And the answer is:
p = 20
So, p has decided to make a grand entrance at the party, and it's the fabulous number 20!
4. 3(1 - 2k) = -5k
Oh boy, this equation is multiplying and subtracting, it's a mathematical roller coaster! But don't you worry, I'll strap myself in and solve this crazy ride.
First, let's simplify that expression inside the parentheses:
3(1 - 2k) = -5k
3(1) - 3(2k) = -5k
3 - 6k = -5k
Now let's add 5k to both sides to bring that k together:
3 - 6k + 5k = -5k + 5k
Simplify:
3 - k = 0
To find the value of k, let's subtract 3 from both sides:
3 - k - 3 = 0 - 3
Simplify:
-k = -3
Finally, let's multiply both sides by -1 to make that k positive:
-k * -1 = -3 * -1
And the answer is:
k = 3
So, after riding the mathematical roller coaster, we've arrived at the answer of k being a thrilling 3!
5. 3n + 2 = 8 + 2n
Oh, look at this equation, n's playing hide and seek with those numbers! But don't worry, I'll help you catch n in no time.
Let's gather all the n terms on one side of the equation:
3n - 2n = 8 - 2
Simplify:
n = 6
And just like that, we've caught n red-handed, and it equals the sneaky number 6!
6. -9 - 6(w + 5)
Hmm, this expression seems like a math problem dressed up as a puzzle. But worry not, I'll untangle it for you!
Let's start by simplifying the expression inside the parentheses:
-9 - 6(w + 5)
-9 - 6w - 30
Now let's combine like terms:
-39 - 6w
And that's the final answer. The expression -9 - 6(w + 5) simplifies to a very interesting -39 - 6w!
7. 4(y - 4) = 8
Ah, the mysteries of y and 4, tangled up in an equation. Don't you worry, I'll help unravel this enigma.
Let's start by distributing the 4 to both terms inside the parentheses:
4 * y - 4 * 4 = 8
Simplify:
4y - 16 = 8
Now let's add 16 to both sides to balance things out:
4y - 16 + 16 = 8 + 16
Simplify:
4y = 24
Finally, let's divide both sides by 4 to isolate y:
(4y)/4 = 24/4
And the answer is:
y = 6
So, after a bit of equation magic, y reveals itself to be the marvelous number 6!
8. x + 8 < -28
Oh, this inequality is telling a sad story of less than. But don't worry, I'll brighten things up and find the solution!
Let's subtract 8 from both sides to balance it out:
x + 8 - 8 < -28 - 8
Simplify:
x < -36
And just like that, x is feeling a bit negative and decides it wants to be less than -36!
9. d/13 >= -3
Ah, this inequality brings some sense of greater than or equal to into the equation. Don't worry, I'll help you uncover its secrets.
Let's multiply both sides by 13 to get rid of that pesky fraction:
(d/13) * 13 >= -3 * 13
Simplify:
d >= -39
And just like that, d reveals itself to be greater than or equal to -39!
10. -8x > -64
Oh, this inequality looks like it's flipping the script with that negative coefficient. Let's dive in and find the solution!
First, let's divide both sides by -8 to solve for x:
(-8x)/-8 < (-64)/-8
Remember, dividing by a negative number flips the inequality sign:
x < 8
So, x ends up being smaller than 8, just like an improper fraction!
11. Which inequality matches the graph?
Alright, let's put on our detective hats and match that sneaky graph to its corresponding inequality.
Based on the information given, the correct answer is:
3x + 1 > 4
Because that graph seems to be pointing upwards and reaching for values greater than 4!
12. Which inequality matches the graph?
Time to put those detective hats back on and match this graph to its perfect inequality partner.
Based on what we can see, the correct answer is:
5p - 4 > 14
Because that graph seems to be reaching for values greater than 14, just like my reaching for another bag of popcorn at the movies!
13. Describe the number of solutions for the equation.
5(x - 9) = 5x
Ah, the number of solutions, intriguing! Let me use my math magic to find the answer.
Let's simplify the equation:
5x - 45 = 5x
Now, notice that we have an x on both sides of the equation. When we subtract 5x from both sides, something peculiar happens:
-45 = 0
Uh-oh, this is a problem! We've got a contradiction here. The equation -45 = 0 is simply not true. So, the equation has:
No Solution.
Looks like we've stumbled upon a math mystery that can't be solved. It's like trying to find the punchline to a joke that doesn't exist!
14. Describe the number of solutions for the equation.
-3(x - 5) = 3x + 9
Oh, the number of solutions, that's a mathematical puzzle! Let me put on my thinking cap and find the answer!
Let's simplify the equation:
-3x + 15 = 3x + 9
Now, let's gather all the x terms on one side of the equation:
-3x - 3x = 9 - 15
-6x = -6
If we divide both sides by -6, we get:
x = 1
And just like that, we've found a single solution! The equation has:
One Solution.
It's like finding the punchline to a joke, one solution is all you need for a good laugh!
15. Solve the equation.
3x + 6 = 9
Ah, a classic equation with a twist of addition and multiplication! Let's unravel the mystery of x.
Let's start by subtracting 6 from both sides:
3x + 6 - 6 = 9 - 6
Simplify:
3x = 3
To find x, let's divide both sides by 3:
(3x)/3 = 3/3
And the answer is:
x = 1
So, after a bit of math magic, x steps up and reveals itself to be the delightful number 1!
16. Solve the equation.
R/6 - 3 = 1
Oh, the good old equation disguised with fractions and subtraction. Let me unravel it for you!
Let's start by adding 3 to both sides:
R/6 - 3 + 3 = 1 + 3
Simplify:
R/6 = 4
To find the value of R, let's multiply both sides by 6:
(R/6) * 6 = 4 * 6
And the answer is:
R = 24
So, after a bit of equation magic, R steps forward with a grand entrance, and it's the marvelous number 24!
17. Solve the inequality.
9x < 72
Ah, this inequality is telling us that 9x wants to be less than 72. Let's help it out!
To solve for x, let's divide both sides by 9:
(9x)/9 < 72/9
Simplify:
x < 8
So, x decides to be a dreamer and choose smaller values than 8. It's like aiming for a lower high-five!