Question 502863: 5z+6/6+6z-10/30=z-5/5
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! 5z+(6)/(6)+6z-(10)/(30)=z-(5)/(5)
Cancel the common factor of 6 in (6)/(6).
5z+(6)/(6)+6z-(10)/(30)=z-(5)/(5)
Remove the common factors that were cancelled out.
5z+1+6z-(10)/(30)=z-(5)/(5)
Cancel the common factor of 10 in -(10)/(30) since -(10)/(30)=((-1*10))/((3*10)).
5z+1+6z-(10)/(330)=z-(5)/(5)
Remove the common factors that were cancelled out.
5z+1+6z-(1)/(3)=z-(5)/(5)
According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, z is a factor of both 5z and 6z.
(5+6)z+1-(1)/(3)=z-(5)/(5)
Add 6 to 5 to get 11.
(11)z+1-(1)/(3)=z-(5)/(5)
Remove the parentheses.
11z+1-(1)/(3)=z-(5)/(5)
Cancel the common factor of 5 in -(5)/(5).
11z+1-(1)/(3)=z-(5)/(5)
Remove the common factors that were cancelled out.
11z+1-(1)/(3)=z-1
Since z contains the variable to solve for, move it to the left-hand side of the equation by subtracting z from both sides.
11z+1-(1)/(3)-z=-1
According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, z is a factor of both 11z and -z.
(11-1)z+1-(1)/(3)=-1
To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of 11 and -1 and give the result the same sign as the integer with the greater absolute value.
(10)z+1-(1)/(3)=-1
Remove the parentheses.
10z+1-(1)/(3)=-1
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 3. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
10z+1*(3)/(3)-(1)/(3)=-1
Multiply 1 by 3 to get 3.
10z+(3)/(3)-(1)/(3)=-1
Combine the numerators of all fractions that have common denominators.
10z+(3-1)/(3)=-1
Subtract 1 from 3 to get 2.
10z+(2)/(3)=-1
Since (2)/(3) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (2)/(3) from both sides.
10z=-(2)/(3)-1
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 3. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
10z=-1*(3)/(3)-(2)/(3)
Multiply -1 by 3 to get -3.
10z=-(3)/(3)-(2)/(3)
Combine the numerators of all fractions that have common denominators.
10z=(-3-2)/(3)
Subtract 2 from -3 to get -5.
10z=(-5)/(3)
Move the minus sign from the numerator to the front of the expression.
10z=-(5)/(3)
Divide each term in the equation by 10.
(10z)/(10)=-(5)/(3)*(1)/(10)
Cancel the common factor of 10 in (10z)/(10).
(10z)/(10)=-(5)/(3)*(1)/(10)
Remove the common factors that were cancelled out.
z=-(5)/(3)*(1)/(10)
Cancel the common factor of 5 from the numerator of the first term -(5)/(3) and the denominator of the second term (1)/(10).
z=-(5)/(3)*(1)/(102)
Remove the common factor of 5 from the numerator of the first term -(5)/(3) and the denominator of the second term (1)/(10).
z=-(1)/(3)*(1)/(2)
Multiply -1 by 1 to get -1.
z=-(1)/(2*3)
Multiply 3 by 2 to get 6.
z=-(1)/(6)
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