show me the steps to solving this problem?
3k/5+44=12k/25+8
multiply each term by 25, the common denominator, to clean up the fractions
15k + 1100 = 12k + 200
3k = -900
k = -300
check:
3(-300)/5 + 44 = -136
12(-300)/25 + 8 = -136
Yeah!
To solve the equation 3k/5 + 44 = 12k/25 + 8, follow these steps:
Step 1: Begin by simplifying both sides of the equation if possible. To do this, you can find a common denominator for the fractions.
On the left side: 3k/5 remains the same.
On the right side: Since 25 is the least common denominator between 25 and 5, we need to multiply 8 by 5/5 to get 40/5.
Now, the equation becomes: 3k/5 + 44 = 12k/25 + 40/5.
Step 2: Next, we can simplify the equation further by multiplying through by the common denominator to eliminate fractions. In this case, our common denominator is 25.
Multiply both sides of the equation by 25 to get:
(25 * 3k/5) + (25 * 44) = (25 * 12k/25) + (25 * 40/5).
Simplifying further, we have:
15k + 1100 = 12k + 200.
Step 3: Now, we want to isolate the variable k on one side of the equation. Start by combining like terms on both sides. In this case, combine 15k and 12k on the left side:
15k - 12k + 1100 = 12k - 12k + 200.
Simplifying further, we have:
3k + 1100 = 200.
Step 4: Continue isolating the variable by subtracting 1100 from both sides of the equation:
3k + 1100 - 1100 = 200 - 1100.
Simplifying further, we have:
3k = -900.
Step 5: Lastly, solve for k by dividing both sides of the equation by 3:
(3k)/3 = (-900)/3.
Simplifying further, we have:
k = -300.
Therefore, the solution to the equation 3k/5 + 44 = 12k/25 + 8 is k = -300.