1. Is the equation true, false, or open?
5x+2=6x+11
a. Open; there is a variable
b. True; the expressions are the same for all values of the variables
c. False; the expressions are never the same
2. Which equation is an identity?
a. 8-(5x+2)=-5x-6
b. 7z+10-z=8z-2(z-5)
c. 8m-4=5m+8-m
d. 6y+5=6y-5
3. Which equation has no solution?
a. 3x-5=3x+8-x
b. 4y+5=4y-6
c. 7z+6=-7z-5***
4. How do I solve these types of problems? (I need steps on how to solve)
4(x-3)+5=1
96=-6(-4-3y)
-2+4=2(4x-3)-3(-8+4x)
-5=s-3
5/13t=-9
6=x+2/3
13+w/7=-18
17=-13-8x
5. What is an estimate of the solution of the equation 6n+3=2? Use a table.
If anyone could help me on these problems, I would really appreciate it.
Here is a nice website that shows steps that you asked for in #4 - I am not allowed to post it. Do a google search of solving linear equations and look for one related to NYS regents.
If you can solve for the variable, the equation is open.
If you eliminate all of the variables and have a statement like 2 =2 This is true which means any variable replacement will work and can be called an identity.
If you eliminate all of the variables and have a statement like -2 = 2 this is false and there is no solution.
u said it lol
haha fr
1. The equation 5x + 2 = 6x + 11 is an open equation because it contains a variable (x) that can take different values.
2. An identity equation is an equation that is true for all values of the variable. Let's analyze the given options:
a. 8 - (5x + 2) = -5x - 6: This equation simplifies to 6 - 5x = -5x - 6, which is not true for all values of x.
b. 7z + 10 - z = 8z - 2(z - 5): This equation simplifies to 6z + 10 = 8z - 2z + 10, which is true for all values of z.
c. 8m - 4 = 5m + 8 - m: This equation simplifies to 7m - 4 = 8, which is not true for all values of m.
d. 6y + 5 = 6y - 5: This equation simplifies to 10 = -5, which is not true for any value of y.
Therefore, the equation 7z + 10 - z = 8z - 2(z - 5) is the identity equation.
3. To determine which equation has no solution, let's examine the options:
a. 3x - 5 = 3x + 8 - x: This equation simplifies to -5 = 8, which is not true and does not have a solution.
b. 4y + 5 = 4y - 6: This equation simplifies to 11 = -6, which is not true and does not have a solution.
c. 7z + 6 = -7z - 5: This equation simplifies to 14z = -11, which is also not true and does not have a solution.
Therefore, the equation 7z + 6 = -7z - 5 has no solution.
4. To solve equations like the ones provided, follow these steps:
a. Solve 4(x-3) + 5 = 1:
Distribute the 4: 4x - 12 + 5 = 1
Combine like terms: 4x - 7 = 1
Move the constant term to the other side by adding 7: 4x = 1 + 7
Simplify: 4x = 8
Divide both sides by 4 to isolate x: x = 8/4
Simplify: x = 2
b. Solve 96 = -6(-4 - 3y):
Simplify inside parentheses: 96 = -6(-4 - 3y)
Multiply -6 by each term inside the parentheses: 96 = 24 + 18y
Combine like terms: 96 = 24 + 18y
Move the constant term to the other side by subtracting 24: 96 - 24 = 24 + 18y - 24
Simplify: 72 = 18y
Divide both sides by 18 to isolate y: 72/18 = 18y/18
Simplify: 4 = y
c. Solve -2 + 4 = 2(4x - 3) - 3(-8 + 4x):
Simplify expressions inside parentheses: -2 + 4 = 2(4x - 3) - 3(-8 + 4x)
Combine like terms: 2 = 2(4x - 3) + 24 - 12x
Distribute the 2: 2 = 8x - 6 + 24 - 12x
Combine like terms: 2 = -4x + 18
Move the constant term to the other side by subtracting 18: 2 - 18 = -4x + 18 - 18
Simplify: -16 = -4x
Divide both sides by -4 to isolate x: -16/-4 = -4x/-4
Simplify: 4 = x
Continue the same process for the remaining equations.
5. To estimate the solution of the equation 6n + 3 = 2 using a table, you can assign different values to n and evaluate the equation for each value. Consider the following table:
| n | 6n + 3 |
|----|--------|
| -2 | -9 |
| -1 | -3 |
| 0 | 3 |
| 1 | 9 |
| 2 | 15 |
From the table, we can see that as we approach n = -1, the expression 6n + 3 gets closer to 2. Therefore, our estimate for the solution is n ≈ -1.