Answer:
- <u>5</u><u> </u>is the value which makes the equation true .
Step-by-step explanation:
In this question we have provided an equation that is <u>9</u><u> </u><u>(</u><u> </u><u>3x</u><u> </u><u>-</u><u> </u><u>1</u><u>6</u><u> </u><u>)</u><u> </u><u>+</u><u> </u><u>1</u><u>5</u><u> </u><u>=</u><u> </u><u>6</u><u>x</u><u> </u><u>-</u><u> </u><u>2</u><u>4</u><u> </u>. And we are asked to <u>write </u><u>the </u><u>steps </u><u>to </u><u>solve </u><u>the </u><u>equation </u><u>with </u><u>explanation </u> and <u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>X </u><u>.</u>
<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>
![\longmapsto \quad \: 9(3x - 16) + 15 = 6x - 24](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A%209%283x%20-%2016%29%20%2B%2015%20%3D%206x%20-%2024)
<u>Step </u><u>1</u><u> </u><u>:</u> Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :
![\longmapsto \quad \:27x - \bold{144 }+ \bold{15 }= 6x - 24](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A27x%20-%20%20%5Cbold%7B144%20%7D%2B%20%20%5Cbold%7B15%20%7D%3D%206x%20-%2024)
<u>Step </u><u>2</u><u> </u><u>:</u> Solving like terms on left side that are -144 and 15 :
![\longmapsto \quad \:27x -129 = 6x - 24](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A27x%20-129%20%3D%206x%20-%2024)
<u>Step </u><u>3 </u><u>:</u> Adding 129 on both sides :
![\longmapsto \quad \:27x - \cancel{129} - \cancel{129} = 6x \bold{ - 24 } + \bold{129}](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A27x%20-%20%5Ccancel%7B129%7D%20-%20%20%5Ccancel%7B129%7D%20%3D%206x%20%5Cbold%7B%20-%2024%20%7D%20%2B%20%20%5Cbold%7B129%7D)
Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :
![\longmapsto \quad \:27x = 6x + 105](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A27x%20%3D%206x%20%2B%20105)
<u>Step </u><u>4</u><u> </u><u>:</u> Subtracting with 6x on both sides :
![\longmapsto \quad \: \bold{27x} - \bold{6x} = \cancel{6x} +105 - \cancel{ 6x}](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A%20%5Cbold%7B27x%7D%20-%20%20%5Cbold%7B6x%7D%20%3D%20%20%5Ccancel%7B6x%7D%20%2B105%20-%20%5Ccancel%7B%206x%7D)
On calculating further, We get :
![\longmapsto \quad \:21x = 105](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A21x%20%3D%20%20105)
<u>Step </u><u>5</u><u> </u><u>:</u> Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :
![\longmapsto \quad \: \dfrac{ \cancel{21}x}{ \cancel{21}} = \dfrac{105}{ 21}](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A%20%5Cdfrac%7B%20%5Ccancel%7B21%7Dx%7D%7B%20%5Ccancel%7B21%7D%7D%20%20%3D%20%5Cdfrac%7B105%7D%7B%2021%7D%20)
Now , by cancelling 21 with 21 on left side , We get :
![\longmapsto \quad \:x = \cancel{\dfrac{105}{21}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3Ax%20%3D%20%20%5Ccancel%7B%5Cdfrac%7B105%7D%7B21%7D%7D%20)
<u>Step </u><u>6</u><u> </u><u>:</u> Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :
![\longmapsto \quad \: \purple{\underline{\boxed{\frak{ x = 5 }}}}](https://tex.z-dn.net/?f=%20%5Clongmapsto%20%5Cquad%20%5C%3A%20%20%20%20%5Cpurple%7B%5Cunderline%7B%5Cboxed%7B%5Cfrak%7B%20x%20%3D%20%205%20%7D%7D%7D%7D)
- <u>Henceforth</u><u> </u><u>,</u><u> </u><u>value </u><u>of </u><u>x </u><u>is </u><u>5</u>
<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>
Now we are verifying our answer by substituting value of x in the given equation . So ,
- 9 ( 3x - 16 ) + 15 = 6x - 24
- 9 [ 3 ( 5 ) - 16 ] + 15 = 6 ( 5 ) - 24
- 9 ( 15 - 16 ) + 15 = 30 - 24
<u>Therefore</u><u>,</u><u> our</u><u> value</u><u> for</u><u> x</u><u> is</u><u> correct</u><u> </u><u>that </u><u>means</u><u> </u><u>it'll</u><u> </u><u>makes</u><u> </u><u>the </u><u>equation</u><u> true</u><u> </u><u>.</u>
<h2>
<u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>