1) The value of n is 2
2) The best interpretation of equation 2/3(6x – 3) =1/2 is the equation has one solution: x = 0
3) The solution to equation y + 3 = -y + 9 is y = 6
4) The value of x is 4
5) The solution to a linear equation 2/5 + p = 4/5 + 3/5p is p = 1
6) The solution to an equation - 9x + 1 = - x + 17 is x = -2
7) A number line represents the solutions to -2|x| = -6 is option 4
1) We have been given an equation 1/2(n-4) - 3 = 3 - (2n+3)
We need to find the value of n.
1/2(n - 4) - 3 = 3 - (2n+3)
1/2(n - 4) = -2n + 3
n - 4 = -4n + 6
5n = 10
n = 2
2) In this question Kate begins solving the equation 2/3(6x – 3) =1/2 as:
2/3(6x – 3) = 1/2(6x – 4)
4x – 2 = 3x – 2
4x = 3x
We need to find the best interpretation of this equation.
4x - 3x = 0
x=0
Thus, the best interpretation of this equation is the equation has one solution: x = 0
3) In this question we need to solve an equation y + 3 = -y + 9
y + y = 9 + 3
2y = 12
y = 6
4) In this question we need to find the value of x for an inequality 2x - 3 > 11 - 5x
2x - 3 > 11 - 5x
2x + 5x > 11 + 3
7x > 14
x > 2
As x > 2, the value of x is 4.
5) We need to find the solution to a given linear equation.
Consider a linear equation,
2/5 + p = 4/5 + 3/5p
p - 3/5p = 4/5 - 2/5
2/5p = 2/5
p = 1
Thus, the solution to a given linear equation is p = 1
6) In this question, we need to solve an equation - 9x + 1 = - x + 17
- 9x + x + 1 = - x + 17 + x
-8x = 17 - 1
-8x = 16
x = 16/(-8)
x = -2
7) In this question, we have been given an equation -2|x| = -6
Divide both sides by -2.
|x| = 3
The absolute value of x is 3. It means the value if is either 3 or -3.
In the given figure the blue dot represent the solutions of the given equation.
Only option 4 represent the solution at x=3 and x=-3.
Therefore the correct option is 4.
Learn more about an equation here:
https://brainly.com/question/649785
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Given questions are incomplete.
1) Find the complete question in attachment.
2) Kate begins solving the equation 2/3(6x – 3) =1/2 (6x – 4). Her work is correct and is shown below. 2/3(6x – 3) = 1/2(6x – 4) 4x – 2 = 3x – 2 When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation? The equation has infinite solutions. The equation has one solution: x = 0. The equation has one solution: x = 4/3. The equation has no solution.
3) Solve the equation. y + 3 = -y + 9
y = 1, y = 3, y = 6, y = 9
4) What value of x is in the solution set of 2x - 3 > 11 - 5x?
-3, 0, 2, 4
5) To better understand the problem see the attached figure.
6) Solve the equation. - 9x + 1 = - x + 17
x = -8, x = -2, x = 2, x = 8
7) Which number line represents the solutions to –2|x| = –6?
Find the options are in the attached figure.
