14-w/8=3w/4-21
Please help me solve this and show work
multiply by 8 to clear fractions:
112 - w = 6w - 168
7w = 280
w = 40
To solve the equation 14 - w/8 = 3w/4 - 21, we need to simplify, gather like terms, and isolate the variable w on one side of the equation. Here's how you can do it step by step:
1. Multiply every term in the equation by 8 to eliminate the denominator, making the equation easier to work with:
8(14 - w/8) = 8(3w/4 - 21)
This gives us: 112 - w = 6w - 168
2. Move all the terms with w to one side of the equation and the constant terms to the other side. We can do this by adding w to both sides and adding 168 to both sides:
112 - w + w + 168 = 6w - w + 168 + 168
Simplifying further, we get: 280 = 5w + 336
3. Now, subtract 336 from both sides of the equation to isolate 5w:
280 - 336 = 5w + 336 - 336
Simplifying, we have: -56 = 5w
4. Finally, divide both sides of the equation by 5 to solve for w:
(-56)/5 = 5w/5
This gives us: -11.2 = w
So, the solution to the equation is w = -11.2.
To check your answer, you can substitute -11.2 for w in the original equation and see if both sides are equal.