Question

help me guys
iam struggling to complete this maths h. w
class 8​

Answer 1

Question 1 :

• $\sf\:3x=2x+18$

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Solution :

$\sf\:3x=2x+18$

Transposing +2x to LHS it becomes -2x

$\sf\implies\:3x-2x=18$

$\sf\implies\:1x=18$

$\small{\underline{\boxed{\mathrm{\implies\:x=18}}}}$ $\sf\color{teal}{\bigstar}$

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Verification :

Plugging the value of x as 18

$\sf\:3x=2x+18$

$\sf\dashrightarrow\:3(18)=2(18)+18$

$\sf\dashrightarrow\:54=36+18$

$\sf\dashrightarrow\:54=54$

$\bf\dashrightarrow\:LHS~=~RHS$

Hence Verified !~

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Question 2 :

• $\sf\:5t-3=3t-5$

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Solution :

$\sf\:5t-3=3t-5$

Transposing +3t to LHS it becomes -3t

$\sf\implies\:5t-3t-3=-5$

$\sf\implies\:2t-3=-5$

Transposing -3 to RHS it becomes +3

$\sf\implies\:2t=-5+3$

$\sf\implies\:2t=-2$

Transposing 2 in RHS it goes to the denominator

$\sf\implies\:t=\frac{-2}{2}$

Reducing the fraction to lower terms

$\sf\implies\:t=\cancel{\frac{-2}{2}}$

$\small{\underline{\boxed{\mathrm{\implies\:t=(-1)}}}}$ $\sf\color{teal}{\bigstar}$

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Verification :

Plugging the value of t as (-1)

$\sf\:5t-3=3t-5$

$\sf\dashrightarrow\:5(-1) -3=3(-1) -5$

$\sf\dashrightarrow\:(-5)-3=(-3)-5$

$\sf\dashrightarrow\:-8=-8$

$\bf\dashrightarrow\:LHS~=~RHS$

Hence Verified !~

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Question 3 :

• $\sf\:4z+3=6+2z$

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Solution :

$\sf\:4z+3=6+2z$

Transposing +2z to LHS it becomes -2z

$\sf\implies\:4z-2z+3=6$

$\sf\implies\:2z+3=6$

Transposing +3 to RHS it becomes -3

$\sf\implies\:2z=6-3$

$\sf\implies\:2z=3$

Transposing 2 in RHS it goes to the denominator

$\small{\underline{\boxed{\mathrm{\implies\:z=\frac{3}{2}}}}}$ $\sf\color{teal}{\bigstar}$

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Verification :

Plugging the value of z as 3/2

$\sf\:4z+3=6+2z$

$\sf\dashrightarrow\:4(\frac{3}{2}) +3=6+2(\frac{3}{2})$

$\sf\dashrightarrow\:\cancel{\frac{12}{2}} +3=6+\cancel{\frac{6}{2}}$

$\sf\dashrightarrow\:6 +3=6+3$

$\sf\dashrightarrow\:9=9$

$\bf\dashrightarrow\:LHS~=~RHS$

Hence Verified !~

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Question 4 :

• $\sf\:2x-1=14-x$

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Solution :

$\sf\:2x-1=14-x$

Transposing -x to LHS it becomes +x

$\sf\implies\:2x+x-1=14$

$\sf\implies\:3x-1=14$

Transposing -1 to RHS it becomes +1

$\sf\implies\:3x=14+1$

$\sf\implies\:3x=15$

Transposing 3 in RHS it goes to the denominator

$\sf\implies\:x=\frac{15}{3}$

Reducing the fraction to lower terms

$\sf\implies\:x=\cancel{\frac{15}{3}}$

$\small{\underline{\boxed{\mathrm{\implies\:x=5}}}}$ $\sf\color{teal}{\bigstar}$

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Verification :

Plugging the value of x as 5

$\sf\:2x-1=14-x$

$\sf\dashrightarrow\:2(5) -1=14-5$

$\sf\dashrightarrow\:10-1=9$

$\sf\dashrightarrow\:9=9$

$\bf\dashrightarrow\:LHS~=~RHS$

Hence Verified !~

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Hope it helps you :D~

Answer 2

Alchemy is defined as the process of taking something ordinary and turning it into something extraordinary, sometimes in a way that cannot be explained. An example of using alchemy is a person who takes a pile of scrap metal and turns it into beautiful art.