Question

solve the following questions and verify the result.do in your copy please​

Answer 1

$\large\sf\underline{Given\::}$

• $\bf\:\frac{x-3}{2}-\frac{x-1}{5}=\frac{2x-3}{5}$

‎

$\large\sf\underline{To\:find\::}$

• The value of x.

‎

$\large\sf\underline{Solution\::}$

$\sf\:\frac{x-3}{2}-\frac{x-1}{5}=\frac{2x-3}{5}$

• LCM of 2 and 5 = 10

$\sf\implies\:\frac{5(x-3)-2(x-1)}{10}=\frac{2x-3}{5}$

• Multiplying the terms in the numerator in LHS

$\sf\implies\:\frac{5x-15-(2x-2)}{10}=\frac{2x-3}{5}$

• Removing the brackets in the numerator in LHS

$\sf\implies\:\frac{5x-15-2x+2}{10}=\frac{2x-3}{5}$

• Doing simple calculations in numerator with like terms

$\sf\implies\:\frac{3x-13}{10}=\frac{2x-3}{5}$

• Cross multiplying

$\sf\implies\:10(2x-3) =5(3x-13)$

$\sf\implies\:20x-30=15x-65$

• Transposing +15x to LHS it becomes -15x

$\sf\implies\:20x-15x-30=-65$

$\sf\implies\:5x-30=-65$

• Transposing -30 to RHS it becomes +30

$\sf\implies\:5x=-65 +30$

$\sf\implies\:5x=-35$

• Transposing 5 to the RHS it goes to the denominator

$\sf\implies\:x=\frac{-35}{5}$

• Reducing the fraction

$\sf\implies\:x=\cancel{\frac{-35}{5}}$

$\small{\underline{\boxed{\mathrm\red{{\mathfrak{\implies\:x\:=\:-7}}}}}}$ ★

‎

$\large\sf\underline{Verifying\::}$

We got our final answer as ( - 7 ) . So let's check if it is correct. For checking we would substitute the value of x as ( - 7 ) in the given equation. Doing so if we get LHS = RHS, our answer would be correct. Let's do!

$\sf\:\frac{x-3}{2}-\frac{x-1}{5}=\frac{2x-3}{5}$

• Substituting the value of x as ( - 7 )

$\sf\rightarrow\:\frac{(-7)-3}{2}-[\frac{(-7)-1}{5}]=\frac{2(-7)-3}{5}$

$\sf\rightarrow\:\frac{-7-3}{2}-[\frac{-7-1}{5}]=\frac{2 \times (-7)-3}{5}$

$\sf\rightarrow\:\frac{-10}{2}-[\frac{-8}{5}]=\frac{(-14)-3}{5}$

$\sf\rightarrow\:\frac{-10}{2}+\frac{8}{5}=\frac{-17}{5}$

$\sf\rightarrow\:\frac{[5 \times (-10) ]+[2 \times 8]}{10}=\frac{-17}{5}$

$\sf\rightarrow\:\frac{(-50) + 16}{10}=\frac{-17}{5}$

$\sf\rightarrow\:\frac{-34}{10}=\frac{-17}{5}$

$\sf\rightarrow\:\cancel{\frac{-34}{10}}=\frac{-17}{5}$

$\sf\rightarrow\:\frac{-17}{5}=\frac{-17}{5}$

$\bf\rightarrow\:LHS=RHS$

$\bf\color{green}{Hence~Verified~!! }$

______________________________

Note :- I have‎ provided you the answer both in attachment and in typed form . Refer to whichever you are comfortable with :D

‎

!! Hope it helps !!