Simplify the Expressions
1) -4(3x-3) + 9(x+1)= -3x21
2) -9x(5x+4)+10(x+3)= -45x-26 x+3
3) n(1+ 10n)-n(4n-3)= 4n+6n
4) -2n(-8n-10)-6(-10n-3)= 96n - 10
5) 8(-4x-7)+3(9-9x)= 59x - 29
6) 9(3-10n)-3(10n+1)= 30n - 3
7) -4(1-8x)-9(-10x-1)= -58 - 5
wow, can you at least do one, so I can see where you problem lies ?
I did, just want you to check my answer
-4(3x-3)+9(x+1)
To simplify these expressions, we will follow the order of operations (also known as PEMDAS or BODMAS).
1) -4(3x-3) + 9(x+1) = -3x21
To simplify this expression, start by applying the distributive property:
-4 * 3x - 4 * (-3) + 9 * x + 9 * 1 = -3x21
Simplify further:
-12x + 12 + 9x + 9 = -3x21
Combine like terms:
-3x + 21 = -3x21
Since the equation -3x21 is not possible, there is no valid solution for this expression.
2) -9x(5x+4) + 10(x+3) = -45x - 26x + 3
Again, apply the distributive property:
-9x * 5x - 9x * 4 + 10x + 10 * 3 = -45x - 26x + 3
Simplify further:
-45x^2 - 36x + 10x + 30 = -45x - 26x + 3
Combine like terms:
-45x^2 - 26x + 30 = -45x - 26x + 3
Move all terms to one side:
-45x^2 - 26x + 45x + 26x + 30 - 3 = 0
Combine like terms:
-45x^2 + 45x + 27 = 0
This equation can be simplified no further, so the expression remains as -45x^2 + 45x + 27.
3) n(1+10n) - n(4n-3) = 4n + 6n
Again, apply the distributive property:
n * 1 + n * 10n - n * 4n + n * 3 = 4n + 6n
Simplify further:
n + 10n^2 - 4n^2 + 3n = 4n + 6n
Combine like terms:
10n^2 - 4n^2 + n + 3n - 4n - 6n = 0
Simplify further:
6n^2 - 6n = 0
Factor out a common factor:
6n(n - 1) = 0
Set each factor to zero:
6n = 0 or n - 1 = 0
Solve for n:
n = 0 or n = 1
The simplified expression is n = 0 or n = 1.
4) -2n(-8n-10) - 6(-10n-3) = 96n - 10
Apply the distributive property:
-2n * -8n - 2n * (-10) - 6 * (-10n) - 6 * (-3) = 96n - 10
Simplify further:
16n^2 + 20n + 60n + 18 = 96n - 10
Combine like terms:
16n^2 + 80n + 18 = 96n - 10
Move all terms to one side:
16n^2 + 80n - 96n + 18 + 10 = 0
Combine like terms:
16n^2 - 16n + 28 = 0
This equation can be simplified no further, so the expression remains as 16n^2 - 16n + 28.
5) 8(-4x-7) + 3(9-9x) = 59x - 29
Apply the distributive property:
8 * -4x + 8 * (-7) + 3 * 9 - 3 * 9x = 59x - 29
Simplify further:
-32x - 56 + 27 - 27x = 59x - 29
Combine like terms:
-32x - 27x + 59x = 56 - 27 + 29
Combine like terms:
0 = 58
This equation has no valid solution, so there is no simplified expression.
6) 9(3-10n) - 3(10n+1) = 30n - 3
Apply the distributive property:
9 * 3 - 9 * 10n - 3 * 10n - 3 * 1 = 30n - 3
Simplify further:
27 - 90n - 30n - 3 = 30n - 3
Combine like terms:
27 - 120n - 3 = 30n - 3
Combine like terms:
24 - 120n = 30n - 3
Move all terms to one side:
24 - 3 = 30n + 120n
Combine like terms:
21 = 150n
Solve for n:
n = 21/150
The simplified expression is n = 21/150.
7) -4(1-8x) - 9(-10x-1) = -58 - 5
Apply the distributive property:
-4 * 1 + 4 * (-8x) - 9 * (-10x) - 9 * (-1) = -58 - 5
Simplify further:
-4 + (-32x) + 90x + 9 = -58 - 5
Combine like terms:
-32x + 90x + 9 - 4 = -58 - 5
Combine like terms:
58x + 5 = -58 - 5
Combine like terms:
58x + 5 = -63
Move all terms to one side:
58x + 63 = 0
This equation can be simplified no further, so the expression remains as 58x + 63.