Question

$\frac{x}{2} - 2 = \frac{x}{3} + 1$
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Answer 1

Answer:

18

Step-by-step explanation:

$\longrightarrow \sf{ \dfrac{x}{2} - 2 = \dfrac{x}{3} + 1 } \\ \\ \longrightarrow \sf{ \dfrac{x - 4}{2} = \dfrac{x}{3} + 1 } \\ \\ \longrightarrow \sf{ \dfrac{x - 4}{2} = \dfrac{x + 3}{3} } \\ \\ \pmb {\rm{by \: cross \: multiplication - }} \\ \\ \\ \longrightarrow \sf{3(x - 4) = 2(x + 3)} \\ \\ \longrightarrow \sf{3x - 12 = 2x + 6} \\ \\ \longrightarrow \sf {3x - 2x =6 + 12 } \\ \\ \longrightarrow \sf \red{x = 18}$

Clarification:

Here, we are given a linear equation. We have to find the value of x. Steps involved :

• Firstly we performed subtraction in LHS .
• Then, we performed addition in RHS.
• After doing this, we used the cross multiplication method to solve the linear equation.
• After that, we performed multiplication.
• At last we transposed like terms and got the value of x.

Verification :

$\longrightarrow\sf{ \dfrac{x}{2} - 2 = \dfrac{x}{3} + 1 }$

L.H.S:

$\longrightarrow \sf { \dfrac{x}{2} - 2 } \\ \\ \longrightarrow \sf { \dfrac{18}{2} - 2 }\\ \\ \sf { 9 - 2 } \\ \\ \longrightarrow\sf \red {7 }$

R.H.S:

$\longrightarrow \sf { \dfrac{x}{3} +1 } \\ \\ \longrightarrow \sf { \dfrac{18}{3} + 1}\\ \\ \longrightarrow \sf { 6+ 1} \\ \\\longrightarrow \sf \red {7 }$

LHS = RHS

Henceforth ,verified !!

Answer 2

Answer:

x = 18

Step-by-step explanation:

$\frac{x}{2} - 2 = \frac{x}{3} + 1 \\ = > \frac{x - 4}{2} = \frac{x + 3}{3} \\ by \: cross \: multiply \: \\ = > 3(x - 4) = 2(x + 3) \\ = > 3x - 12 = 2x + 6 \\ = > 3x - 2x =6 + 12 \\ = > x = 18$

$verification \\ = > \frac{x}{2} - 2 = \frac{x}{3} + 1 \\ = > \frac{18}{2} - 2 = \frac{18}{3} + 1 \\ = > \frac{18 - 4}{2} = \frac{18 + 3}{3} \\ = > \frac{14}{2} = \frac{21}{3} \\ = > 7 = 7 \\ so \: it \: is \: verified.$

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