15: To solve the equation 5x+8+x=32, we can combine like terms by adding the x terms together and subtracting 8 from both sides:
6x + 8 = 32
Next, we can isolate the x term by subtracting 8 from both sides:
6x = 24
To solve for x, we divide both sides of the equation by 6:
x = 4
To check our answer, we substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, we can conclude that x = 4 is the correct solution.
1: Solve for x: -5x = -30
2: Solve for x: 12 - x/9 = 11
3: Solve for x: -20 = -5 +3x
4: solve for x: 20 = 5 - 3/8x
5: Solve for x: 4(x + 7) - 3(x - 5) = 44
6: Solve for x: -8x + 5(2x -10) = -30
7: Solve for x: -2(3x - 15) -25 = 35
8: Solve for x: 12x + 5 = 10x - 11
9: At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.
10: An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.
11: At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point)
The songs will have the same number of listens after __________ days.
12: Which of the following equations has no solutions?(1 point)
Responses
−6x+4=6x+3
6x+3=−6x+3
−6x+4=−6x+3
6x+4=6x+4
13: Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x(1 point)
Responses
The equation has one solution: x=−3.
The equation has one solution: x=−1.
The equation has no solution.
The equation has infinite solutions.
14: Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6(1 point)
The equation has infinite solutions.
The equation has one solution: x=1.
The equation has no solution.
The equation has one solution: x=0.
15: Solve the following linear equation for x . Then check your answer. Show all your steps for solving and checking.
5x+8+x=32
7 answers
answer ALL of the QUESTIONS
Certainly! Here are the solutions to all of the given questions:
1: -5x = -30
To solve for x, divide both sides of the equation by -5:
x = -30 / -5
x = 6
2: 12 - x/9 = 11
To solve for x, subtract 12 from both sides and multiply both sides by 9:
x/9 = 12 - 11
x/9 = 1
x = 9
3: -20 = -5 + 3x
To solve for x, add 5 to both sides and divide both sides by 3:
-20 + 5 = 3x
-15 = 3x
x = -5
4: 20 = 5 - 3/8x
To solve for x, subtract 5 from both sides and multiply both sides by 8/3:
20 - 5 = -3/8x
15 = -3/8x
x = -40
5: 4(x + 7) - 3(x - 5) = 44
To solve for x, distribute and combine like terms:
4x + 28 - 3x + 15 = 44
x + 43 = 44
Subtract 43 from both sides:
x = 1
6: -8x + 5(2x -10) = -30
To solve for x, distribute and combine like terms:
-8x + 10x - 50 = -30
2x - 50 = -30
Add 50 to both sides:
2x = 20
x = 10
7: -2(3x - 15) -25 = 35
To solve for x, distribute and combine like terms:
-6x + 30 - 25 = 35
-6x + 5 = 35
Subtract 5 from both sides:
-6x = 30
x = -5
8: 12x + 5 = 10x - 11
To solve for x, subtract 10x from both sides, then subtract 5 from both sides:
12x - 10x = - 11 - 5
2x = -16
Divide both sides by 2:
x = -8
9: Let x be the number of days.
The equation to show the number of listens for the two songs is:
1000 + 38x = 900 + 40x
10: Let x be the number of visits.
The equation to show the cost of the two plans being equal is:
10x = 32 + 6x
11: Let x be the number of days.
The equation to show when the two songs have the same number of listens is:
700 + 52x = 600 + 56x
12: The equation with no solutions is:
-6x + 4 = -6x + 3
(Both sides have -6x, which cancels out the x term, leaving 4 = 3, which is not true)
13: The equation has one solution: x = -1.
(Simplify both sides to -3 = -3, which is true)
14: The equation has infinite solutions.
(Both sides simplify to 0 = 0, which is true)
Please let me know if you need further assistance!
1: -5x = -30
To solve for x, divide both sides of the equation by -5:
x = -30 / -5
x = 6
2: 12 - x/9 = 11
To solve for x, subtract 12 from both sides and multiply both sides by 9:
x/9 = 12 - 11
x/9 = 1
x = 9
3: -20 = -5 + 3x
To solve for x, add 5 to both sides and divide both sides by 3:
-20 + 5 = 3x
-15 = 3x
x = -5
4: 20 = 5 - 3/8x
To solve for x, subtract 5 from both sides and multiply both sides by 8/3:
20 - 5 = -3/8x
15 = -3/8x
x = -40
5: 4(x + 7) - 3(x - 5) = 44
To solve for x, distribute and combine like terms:
4x + 28 - 3x + 15 = 44
x + 43 = 44
Subtract 43 from both sides:
x = 1
6: -8x + 5(2x -10) = -30
To solve for x, distribute and combine like terms:
-8x + 10x - 50 = -30
2x - 50 = -30
Add 50 to both sides:
2x = 20
x = 10
7: -2(3x - 15) -25 = 35
To solve for x, distribute and combine like terms:
-6x + 30 - 25 = 35
-6x + 5 = 35
Subtract 5 from both sides:
-6x = 30
x = -5
8: 12x + 5 = 10x - 11
To solve for x, subtract 10x from both sides, then subtract 5 from both sides:
12x - 10x = - 11 - 5
2x = -16
Divide both sides by 2:
x = -8
9: Let x be the number of days.
The equation to show the number of listens for the two songs is:
1000 + 38x = 900 + 40x
10: Let x be the number of visits.
The equation to show the cost of the two plans being equal is:
10x = 32 + 6x
11: Let x be the number of days.
The equation to show when the two songs have the same number of listens is:
700 + 52x = 600 + 56x
12: The equation with no solutions is:
-6x + 4 = -6x + 3
(Both sides have -6x, which cancels out the x term, leaving 4 = 3, which is not true)
13: The equation has one solution: x = -1.
(Simplify both sides to -3 = -3, which is true)
14: The equation has infinite solutions.
(Both sides simplify to 0 = 0, which is true)
Please let me know if you need further assistance!
sorry, i forgot to mention that you need to solve x for 10. 10: Let x be the number of visits.
The equation to show the cost of the two plans being equal is:
10x = 32 + 6x
The equation to show the cost of the two plans being equal is:
10x = 32 + 6x
Apologies for the confusion. Let's solve equation 10 for x:
10x = 32 + 6x
To solve for x, we can subtract 6x from both sides:
10x - 6x = 32
Combine like terms:
4x = 32
Next, we divide both sides by 4:
x = 32 / 4
x = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.
Please let me know if there is anything else I can help you with!
10x = 32 + 6x
To solve for x, we can subtract 6x from both sides:
10x - 6x = 32
Combine like terms:
4x = 32
Next, we divide both sides by 4:
x = 32 / 4
x = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.
Please let me know if there is anything else I can help you with!
solve x for 11 too
Certainly! Let's solve equation 11 for x:
Let x be the number of days.
The equation to show when the two songs have the same number of listens is:
700 + 52x = 600 + 56x
To solve for x, we can subtract 600 from both sides:
700 + 52x - 600 = 56x
Combine like terms:
100 + 52x = 56x
Next, subtract 52x from both sides:
100 = 56x - 52x
Combine like terms:
100 = 4x
To isolate x, divide both sides by 4:
x = 100 / 4
x = 25
Therefore, the two songs will have the same number of listens after 25 days.
Please let me know if there is anything else I can assist you with!
Let x be the number of days.
The equation to show when the two songs have the same number of listens is:
700 + 52x = 600 + 56x
To solve for x, we can subtract 600 from both sides:
700 + 52x - 600 = 56x
Combine like terms:
100 + 52x = 56x
Next, subtract 52x from both sides:
100 = 56x - 52x
Combine like terms:
100 = 4x
To isolate x, divide both sides by 4:
x = 100 / 4
x = 25
Therefore, the two songs will have the same number of listens after 25 days.
Please let me know if there is anything else I can assist you with!