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Eduardwww [97]
2 years ago
13

Solve: 3x-5/2 +x+ 2x-3/3 = 5/6 - 3x/2​

Mathematics
2 answers:
torisob [31]2 years ago
6 0

Answer:

<u>Given Question</u>

Solve for x :

\rm :\longmapsto\:\dfrac{3x - 5}{2} + x +  \dfrac{2x - 3}{3} =  \dfrac{5}{6}  - \dfrac{3x}{2}

\green{\large\underline{\sf{Solution-}}}

<u>Given expression is </u>

\rm :\longmapsto\:\dfrac{3x - 5}{2} + x +  \dfrac{2x - 3}{3} =  \dfrac{5}{6}  - \dfrac{3x}{2}

  • On taking LCM of (2 and 3 = 6) on LHS and Taking LCM of ( 2 and 6 = 6) on RHS, we get

\rm :\longmapsto\:\dfrac{3(3x - 5) + 6x + 2(2x - 3)}{6} =  \dfrac{5 - 9x}{6}

\rm :\longmapsto\:9x - 15 + 6x + 4x - 6 =  5 - 9x

\rm :\longmapsto\:(9x + 6x + 4x) - 15 - 6 =  5 - 9x

\rm :\longmapsto\:19x - 21 =  5 - 9x

\rm :\longmapsto\:19x + 9x =  5  + 21

\rm :\longmapsto\:28x =  26

\rm :\longmapsto\:x = \dfrac{26}{28}

\bf\implies \:x = \dfrac{13}{14}

<h3><u>VERIFICATION</u></h3>

<u>Consider LHS </u>

\rm :\longmapsto\:\dfrac{3x - 5}{2} + x +  \dfrac{2x - 3}{3}

On substituting the value of x, we get

\rm \:  =  \: \dfrac{\dfrac{39}{14}  - 5}{2} + \dfrac{13}{14}  +  \dfrac{\dfrac{13}{7}  - 3}{3}

\rm \:  =  \: \dfrac{39- 70}{28} +  \dfrac{13}{14}  +  \dfrac{13 - 21}{21}

\rm \:  =  \: \dfrac{ - 31}{28} +  \dfrac{13}{14}  -  \dfrac{8}{21}

\rm \:  =  \: \dfrac{ - 31 + 26}{28} -  \dfrac{8}{21}

\rm \:  =  \: \dfrac{ -5}{28} -  \dfrac{8}{21}

\rm \:  =  \: \dfrac{ -15 - 32}{84}

\rm \:  =  \: -  \:  \dfrac{47}{84}

<u>Consider RHS</u>

\rm :\longmapsto\: \dfrac{5}{6}  - \dfrac{3x}{2}

On substituting the value of x, we get

\rm \:  =  \:  \dfrac{5}{6}  - \dfrac{39}{28}

\rm \:  =  \:  \dfrac{70 - 117}{84}

\rm \:  =  \: -   \dfrac{47}{84}

Hence, LHS = RHS

<u>Hence, Verified</u><u>.</u>

Vlad [161]2 years ago
3 0

Answer:

x = 26/45

Step-by-step explanation:

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solong [7]

It looks like your equations are

7M - 2t = -30

5t - 12M = 115

<u>Solving by substitution</u>

Solve either equation for one variable. For example,

7M - 2t = -30   ⇒   t = (7M + 30)/2

Substitute this into the other equation and solve for M.

5 × (7M + 30)/2 - 12M = 115

5 (7M + 30) - 24M = 230

35M + 150 - 24M = 230

11M = 80

M = 80/11

Now solve for t.

t = (7 × (80/11) + 30)/2

t = (560/11 + 30)/2

t = (890/11)/2

t = 445/11

<u>Solving by elimination</u>

Multiply both equations by an appropriate factor to make the coefficients of one of the variables sum to zero. For example,

7M - 2t = -30   ⇒   -10t + 35M = -150 … (multiply by 5)

5t - 12M = 115   ⇒   10t - 24M = 230 … (multiply by 2)

Now combining the equations eliminates the t terms, and

(-10t + 35M) + (10t - 24M) = -150 + 230

11M = 80

M = 80/11

It follows that

7 × (80/11) - 2t = -30

560/11 - 2t = -30

2t = 890/11

t = 445/11

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