8(6c-7/4 - 8c-9/8)
To simplify the expression 8(6c - 7/4 - 8c - 9/8), we first distribute the 8 to each term inside the parentheses:
8 * 6c = 48c
8 * (-7/4) = -56/4 = -14
8 * (-8c) = -64c
8 * (-9/8) = -72/8 = -9
Therefore, the simplified expression is:
48c - 14 - 64c - 9.
1/8(n) + 2 = 1/4
To solve the equation 1/8n + 2 = 1/4, we can start by subtracting 2 from both sides:
1/8n + 2 - 2 = 1/4 - 2
This simplifies to:
1/8n = 1/4 - 8/4
Combining the fractions on the right side:
1/8n = -7/4
To isolate n, we can multiply both sides of the equation by 8:
8 * (1/8n) = 8 * (-7/4)
This simplifies to:
n = -56/4
Simplifying further, we get:
n = -14
Therefore, the solution to the equation is n = -14.
8/5(z)-6=12/5(z)+2
To solve the equation 8/5(z) - 6 = 12/5(z) + 2, we can start by simplifying the equation.
First, we can get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of 5 and 5, which is 5:
5 * (8/5(z) - 6) = 5 * (12/5(z) + 2)
This simplifies to:
8z - 30 = 12z + 10
Next, we can isolate the variable terms on one side and the constant terms on the other side. Let's subtract 12z from both sides and add 30 to both sides:
8z - 12z - 30 + 30 = 12z - 12z + 10 + 30
This simplifies to:
-4z = 40
Now, let's divide both sides of the equation by -4 to solve for z:
(-4z) / (-4) = 40 / (-4)
This simplifies to:
z = -10
Therefore, the solution to the equation is z = -10.
1/8(3z-8)-1/9=1/8(z)+1/18
To solve the equation 1/8(3z - 8) - 1/9 = 1/8z + 1/18, we can start by simplifying the equation.
First, let's distribute 1/8 to the expression inside the parentheses:
1/8 * (3z - 8) - 1/9 = 1/8z + 1/18
This simplifies to:
(3z - 8)/8 - 1/9 = 1/8z + 1/18
Next, we need to find a common denominator for the fractions. The LCM of 8 and 9 is 72:
72 * ((3z - 8)/8) - 72 * (1/9) = 72 * (1/8z) + 72 * (1/18)
This simplifies to:
9(3z - 8) - 8 * 8 = 9z + 4z
Expanding and simplifying:
27z - 72 - 64 = 9z + 4z
27z - 136 = 13z
Now, let's isolate the variable terms on one side and the constant terms on the other side. Let's subtract 13z from both sides:
27z - 13z - 136 = 13z - 13z
This simplifies to:
14z - 136 = 0
Now, let's add 136 to both sides:
14z - 136 + 136 = 0 + 136
This simplifies to:
14z = 136
Finally, let's divide both sides by 14 to solve for z:
(14z) / 14 = 136 / 14
This simplifies to:
z = 68/7
Therefore, the solution to the equation is z = 68/7.
1/9(4x+21)=1/3(2x+5)
To solve the equation 1/9(4x + 21) = 1/3(2x + 5), we can start by simplifying the equation.
First, let's distribute 1/9 to the expression inside the parentheses on the left side:
1/9 * (4x + 21) = 1/3(2x + 5)
This simplifies to:
(4x + 21)/9 = (2x + 5)/3
Next, let's find a common denominator for the fractions. The LCM of 9 and 3 is 9:
9 * ((4x + 21)/9) = 9 * ((2x + 5)/3)
This simplifies to:
4x + 21 = 3(2x + 5)
Expanding the right side:
4x + 21 = 6x + 15
Now, let's isolate the variable terms on one side and the constant terms on the other side. Let's subtract 4x from both sides:
4x - 4x + 21 = 6x - 4x + 15
This simplifies to:
21 = 2x + 15
Next, let's subtract 15 from both sides:
21 - 15 = 2x + 15 - 15
This simplifies to:
6 = 2x
Now, let's divide both sides by 2 to solve for x:
6/2 = (2x)/2
This simplifies to:
3 = x
Therefore, the solution to the equation is x = 3.