Solve these fraction equations:
2/3 - 8/9 = c/6
z/3 + 1 = z/2 - 3
Use the distributive property to simplify.
1. -5(a + 2)
for your equations,
multiply the 1st by 18 , the LCM
12 - 16 = 3c
-4 = 3c
c = -4/3
2nd, multiply by 6
2z + 6 = 3z - 18
-z = -24
z = 24
-5(a+2) = -5a - 10
How did you get 3c?
To solve the fraction equations, we'll follow a step-by-step approach.
1. Solve the equation 2/3 - 8/9 = c/6:
First, find a common denominator for 3 and 9, which is 9. Multiply both the numerator and denominator of the first fraction by 3 to get 6/9. The equation becomes 6/9 - 8/9 = c/6.
Now, subtract the fractions: 6/9 - 8/9 = -2/9. The equation is now -2/9 = c/6.
To solve for c, we need to perform cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. -2 * 6 = 9c.
Simplify: -12 = 9c.
Divide both sides of the equation by 9 to isolate c: -12/9 = c. Simplify further: -4/3 = c.
Therefore, the solution to the equation 2/3 - 8/9 = c/6 is c = -4/3.
2. Solve the equation z/3 + 1 = z/2 - 3:
First, let's simplify the equation using the distributive property.
Distribute the 1 to both terms inside the parentheses: z/3 + 1 = z/2 -3 becomes z/3 + 1 = z/2 - 3.
To combine the fractions, we need a common denominator for 3 and 2, which is 6. Multiply the numerator and denominator of the first fraction by 2 to get 2z/6.
The equation is now 2z/6 + 1 = z/2 - 3.
To eliminate the fractions, we'll multiply all terms by 6 to clear the denominators: 6 * (2z/6 + 1) = 6 * (z/2 - 3).
This simplifies to 2z + 6 = 3z - 18.
Next, we'll isolate the variable terms on one side and the constant terms on the other side.
Subtract 2z from both sides: 2z - 2z + 6 = 3z - 2z - 18.
This simplifies to 6 = z - 18.
Now, isolate z by adding 18 to both sides: 6 + 18 = z - 18 + 18.
This simplifies to 24 = z.
Therefore, the solution to the equation z/3 + 1 = z/2 - 3 is z = 24.
3. Use the distributive property to simplify -5(a + 2):
To simplify the expression -5(a + 2), we'll distribute the -5 to both terms inside the parentheses.
Multiply -5 by a: -5 * a = -5a.
Multiply -5 by 2: -5 * 2 = -10.
Therefore, -5(a + 2) simplifies to -5a - 10.