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Hello ~
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[tex]\huge\pmb{\frak{\underline{Answer:}}}[/tex]
[tex]\sf{x = 1}[/tex]
[tex]\huge\pmb{\frak{\underline{Explanation:}}}[/tex]
[tex]\sf{\frac{x}{5} \: + \: \frac{(x \: - \: 1)}{3} = \frac{1}{5}[/tex]
[tex]\sf{\frac{x}{5} \: + \: \frac{x \: - \: 1}{3} = \frac{1}{5}[/tex]
- Find The Least Common Multipler of [tex]\bold{^5^,^3^: \: ^1^5}[/tex]
Multiply by LCM = [tex]\bold{15}[/tex]
[tex]\sf{\frac{x}{5} \: . \: 15 \: + \frac{x \: - \: 1}{3} \: . \: 15 = \frac{1}{5} \: . \: 15}[/tex]
- Simplify :
[tex]\sf{3x \: + \: 5(x \: - \: 1) = 3[/tex]
- Expand [tex]\sf{^5^(^x \: ^- \: ^1^)^: \: ^5^x \: ^- \: ^5}[/tex]
[tex]\sf{3x \: + \: 5x \: - \: 5 = 3}[/tex]
- Add similar elements: [tex]\sf{^3^x \: ^+ \: ^5^x \: ^= \: ^8}[/tex]
[tex]\sf{8x \: - \: 5 \: + \: 5 \: = 3 \: + \: 5}[/tex]
- Simplify :
[tex]\sf{8x \: = \: 8[/tex]
- Divide both sides by [tex]\bold{8}[/tex]
[tex]\sf{\frac{8x}{8} = \frac{8}{8}[/tex]
- Simplify :
[tex]\sf{x = 1}[/tex]
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[tex]\underline{Answer :}[/tex]
ɪ ʀ x ᴅ ꜱ ᴄ ᴇ ɴ ᴛ
Answer:
- x = 1
Step-by-step explanation:
In the question we have given an equation that is x / 5 + ( x - 1 ) / 3 = 1 / 5 . And we are asking to solve the equation that means we have to find the value of x.
Solution : -
[tex] \longmapsto \qquad \dfrac{x}{5} + \dfrac{(x - 1)}{3} = \dfrac{1}{5} [/tex]
Step 1 : Bye taking L.C.M solving left side :
[tex] \longmapsto \qquad \dfrac{3x + 5(x - 1)}{15} = \dfrac{1}{5} [/tex]
On further calculations, We get :
[tex] \longmapsto \qquad \dfrac{3x + 5x - 5}{15} = \dfrac{1}{5} [/tex]
[tex] \longmapsto \qquad \dfrac{8x - 5}{15} = \dfrac{1}{5} [/tex]
Step 2 : Multiplying 15 on both sides :
[tex] \longmapsto \qquad \dfrac{8x - 5}{ \cancel{15}} \times \cancel{15 } = \dfrac{1}{ \cancel{5}} \times \cancel{15}[/tex]
On further calculations, We get :
[tex] \longmapsto \qquad 8x - 5 = 3[/tex]
Step 3 : Adding 5 on both sides :
[tex] \longmapsto \qquad8x - \cancel{5} + \cancel{ 5} = 3 + 5[/tex]
On further calculations, We get :
[tex] \longmapsto \qquad8x = 8[/tex]
Step 4 : Dividing with 8 on both sides :
[tex] \longmapsto \qquad \dfrac{ \cancel{8}x}{ \cancel{8}} = \cancel{\dfrac{8}{8} }[/tex]
On further calculations, We get :
[tex] \longmapsto \qquad \blue{\underline{\blue{\boxed{ \frak{x = 1}}}}}[/tex]
- Henceforth, value of x is 1 .
Verifying : -
We are verifying our answer by substituting value of x in the given equation . So ,
- x / 5 + ( x - 1 ) / 3 = 1 / 5
- 1 / 5 + (1 - 1 ) / 3 = 1 / 5
- 1 / 5 + 0 / 3 = 1 / 5 (0 / 3 is equal to 0)
- 1 / 5 + 0 = 1 / 5
- 1 / 5 = 1 / 5
- L.H.S = R.H.S
- Hence , Verified .
Therefore, our solution is correct .
