Which of the following equations has a solution different from the rest? (1 point) Responses
−0.35x−0.52=1.93 3/4x+5=-1/4 -1/7x-3/4=1/4 1/2x-3=1/2
To determine which equation has a different solution from the rest, we need to solve each equation and compare the solutions.
1) −0.35x−0.52=1.93
Adding 0.52 to both sides:
-0.35x = 2.45
Dividing by -0.35:
x = -7
2) 3/4x+5=-1/4
Subtracting 5 from both sides:
3/4x = -1/4 - 5
Combining fractions:
3/4x = -1/4 - 20/4
3/4x = -21/4
Multiplying both sides by 4/3:
x = -21/4 * 4/3
x = -21/3
x = -7
3) -1/7x-3/4=1/4
Adding 3/4 to both sides:
-1/7x = 1/4 + 3/4
-1/7x = 4/4
-1/7x = 1
Multiplying both sides by -7/1:
x = 1 * -7/1
x = -7
4) 1/2x-3=1/2
Adding 3 to both sides:
1/2x = 1/2 + 3
1/2x = 1/2 + 6/2
1/2x = 7/2
Multiplying both sides by 2:
x = 7/2 * 2
x = 7
From solving each equation, we see that the solution for all the equations is x = -7, except for the fourth equation which has a solution of x = 7. Therefore, the equation that has a different solution from the rest is 1/2x-3=1/2.
Reann has stickers. She gives her friend half, and then her brother gives her 8 new ones. She ends up with 12 stickers. How many did she start with? Identify the operations needed to solve this problem.(1 point)
To solve this problem, we need to use addition and division.
First, we know that Reann gives half of her stickers to her friend. So, we can represent her original number of stickers as x. After giving half to her friend, Reann is left with half of her original stickers, which is x/2.
Next, her brother gives her 8 additional stickers, so her total number of stickers becomes (x/2) + 8.
Finally, we know that Reann ends up with 12 stickers. So we can set up the equation:
(x/2) + 8 = 12
To solve for x, we can subtract 8 from both sides:
(x/2) = 12 - 8
(x/2) = 4
Multiplying both sides of the equation by 2 gives us:
x = 8
Therefore, Reann originally started with 8 stickers.
Sam is buying packages with 9 beads each. His mom bought him 63 more beads. Now, he has 153 beads. How many packages did he buy? Use algebra to determine the answer.(1 point)
To solve this problem, we can set up an equation using algebra.
Let's represent the number of packages Sam bought as x.
Since each package has 9 beads, the total number of beads from the packages is 9x.
His mom bought him an additional 63 beads, so the total number of beads he now has is 9x + 63.
According to the problem, Sam now has 153 beads. We can set up the equation:
9x + 63 = 153
To find the value of x, we can subtract 63 from both sides:
9x = 153 - 63
9x = 90
Lastly, we can divide both sides by 9 to solve for x:
x = 90/9
x = 10
Therefore, Sam bought 10 packages.
Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r . Then write a sentence to explain your answer.
To determine how far Triana will travel on each of the remaining three days, we can set up an equation.
Let's represent the distance Triana will travel on each of the remaining three days as x.
On the first day, she traveled 24 miles.
Over the remaining three days, she wants to travel equal distances, so the total distance traveled on those days would be 3x.
The total distance traveled during the four-day bike ride is 120 miles, so we can set up the equation:
24 + 3x = 120
To solve for x, we can subtract 24 from both sides:
3x = 120 - 24
3x = 96
Lastly, we can divide both sides by 3 to solve for x:
x = 96/3
x = 32
Therefore, Triana will travel 32 miles on each of the remaining three days.
In sentence format, this means that Triana will travel 32 miles on each of the three remaining days of her bike ride, after having traveled 24 miles on the first day.