let's bear in mind that an absolute value expression is in effect a piece-wise expression, namely it has a ± versions of the same expression.
![\bf 5|3x-4| = x+1\implies |3x-4|=\cfrac{x+1}{5}\implies \begin{cases} +(3x-4)=\cfrac{x+1}{5}\\[1em] -(3x-4)=\cfrac{x+1}{5} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ +(3x-4)=\cfrac{x+1}{5}\implies 3x-4=\cfrac{x+1}{5}\implies 15x-20=x+1 \\\\\\ 14x-20=1\implies 14x=21\implies x = \cfrac{21}{14}\implies \boxed{x=\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ -(3x-4)=\cfrac{x+1}{5}\implies -3x+4=\cfrac{x+1}{5}\implies -15x+20=x+1 \\\\\\ 20=16x+1\implies 19=16x\implies \boxed{\cfrac{19}{16}=x}](https://tex.z-dn.net/?f=%5Cbf%205%7C3x-4%7C%20%3D%20x%2B1%5Cimplies%20%7C3x-4%7C%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%2B%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5C%5C%5B1em%5D%20-%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%2B%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%203x-4%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%2015x-20%3Dx%2B1%20%5C%5C%5C%5C%5C%5C%2014x-20%3D1%5Cimplies%2014x%3D21%5Cimplies%20x%20%3D%20%5Ccfrac%7B21%7D%7B14%7D%5Cimplies%20%5Cboxed%7Bx%3D%5Ccfrac%7B3%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20-%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%20-3x%2B4%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%20-15x%2B20%3Dx%2B1%20%5C%5C%5C%5C%5C%5C%2020%3D16x%2B1%5Cimplies%2019%3D16x%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B19%7D%7B16%7D%3Dx%7D)
In this right triangle, you are given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest side of the triangle.
Answer:
3/5 X 3 1/2 = 3/5 X 7/2 = 21/10 = 2.1 in²
Step-by-step explanation:
Take the second equation and flip it around so the y on the left ends up on the right and the 4x on the right ends up on the left. This makes all negatives positive and all positives negative. -4x + 12 = y
Then add the first equation to the second equation
4x +12 = -7y
<u>-4x + 12 </u>=<u> y </u> this eliminates the x's
<u>24</u> = -<u> 6y</u> then divide by - 6
- 6 - 6
- 4 = y<u>
</u>So if you know that y = negative 4, you can substitute into either equation. I pick the second one because I am a lazy person.
-y + 12 = 4 x
-(-4) + 12 = 4 x combine your numbers<u>
</u> <u> 16 </u> = <u>4 x </u> then divide by 4<u>
</u> 4 = x
So your solution is: x = 4 and y = -4 or this is also written (4, -4)
Does that work for you?
Well you see here, you need to take attest pre-calculus to answer this question. I am in 6th grade.
