How do you solve this problem?
3/5k - (k + 1/3) = 1/15 (k + 3)
Please show me the steps. Thanks.
I am not a fan of fractions in equations, so I usually multiply each term by the LCD, in this case 15
9k - 15(k+1/3) = k+3
9k - 15k - 5 = k + 3
-7k = 8
k = -8/7
3/5k - (k + 1/3) = 1/15 (k + 3)
remove ( )
3/5k - k - 1/3 = 1/15k + 3/15
get rid of denominators
since 15 is the LCD of 5, 3, 15
multiplying both sides by 15 will do this
15 (3/5k - k - 1/3) = 15(1/15k + 3/15)
9k - 15k - 5 = k + 3
-6k - 5 = k + 3
-7k = 8
k = -8/7
To solve this problem, we will start by simplifying the equation:
Step 1: Distribute the 1/15 to both terms on the right side of the equation:
3/5k - (k + 1/3) = 1/15k + 1/5
Step 2: Simplify the expression in the parentheses on the left side of the equation:
3/5k - k - 1/3 = 1/15k + 1/5
Step 3: Combine like terms on both sides of the equation:
-2/5k - 1/3 = 1/15k + 1/5
Step 4: Now, we can simplify the equation by getting rid of the fractions. To do this, we will find a common denominator for all the fractions. The common denominator for 5, 3, and 15 is 15:
(-2/5k) * (3/3) - (1/3) * (5/5) = (1/15k) * (15/15) + (1/5) * (3/3)
Simplifying the equation:
-6/15k - 5/15 = 3/15k + 3/15
Step 5: Combine like terms by adding or subtracting the fractions:
-6/15k - 5/15 + 6/15k - 3/15k = 3/15k + 3/15 - 6/15k + 5/15
Simplifying the equation further:
-9/15k - 5/15 = -3/15k + 8/15
Step 6: Combine like terms on both sides of the equation:
-9/15k + 3/15k = 8/15 + 5/15
Simplifying the equation:
-6/15k = 13/15
Step 7: To solve for k, multiply both sides of the equation by -15/6:
(-15/6) * (-6/15k) = (-15/6) * (13/15)
Simplifying the equation:
k = -13/6
Therefore, the solution to the equation is k = -13/6.