3k/4-28-2k/3=37
Please help me solve and show your work please and thank you
multiply 12 by both sides
3 k / 4 - 28 - 2 k / 3 = 37 Multiply both sides by 4
( 3 k / 4 ) * 4 - 28 * 4 - 2 k * 4 / 3 = 37 * 4
3 k - 112 - 8 k / 3 = 148 Multiply both sides by 3
3 k * 3 - 112 * 3 - ( 8 k / 3 ) * 3 = 148 * 3
9 k - 336 - 8 k = 444
9 k - 8 k = 444 + 336
k = 780
To solve the equation 3k/4 - 28 - 2k/3 = 37, we need to simplify the expressions on both sides of the equation and isolate the variable 'k'. Let's follow these steps:
Step 1: Simplify the expressions
- Start by simplifying the fractions: 3k/4 and 2k/3.
- To combine fractions with different denominators, we need to find the least common multiple (LCM) of 4 and 3, which is 12.
- Multiply the numerator and denominator of 3k/4 by 3 to get (9k/12).
- Multiply the numerator and denominator of 2k/3 by 4 to get (8k/12).
The equation then becomes:
(9k/12) - 28 - (8k/12) = 37
Step 2: Combine like terms
- Combine the fractions (9k/12) and (8k/12), which have the same denominator:
(9k/12) - (8k/12) = (k/12)
The equation now becomes:
(k/12) - 28 = 37
Step 3: Isolate the variable 'k'
- To isolate the variable 'k', we need to get rid of the constant term (-28) on the left side of the equation. To do this, we can add 28 to both sides of the equation:
(k/12) - 28 + 28 = 37 + 28
Simplifying, we have:
k/12 = 65
Step 4: Solve for 'k'
- To solve for 'k', we can multiply both sides of the equation by 12 to cancel out the denominator:
(12)(k/12) = (65)(12)
Simplifying further:
k = 780
Hence, the solution to the equation 3k/4 - 28 - 2k/3 = 37 is k = 780.