Question

3/2x-5= 2/x+3, solve for x and verify your answer​

Answer 1

Hello, mate let's get that answer for you!

Answer:

x=5.572599 or x=−0.239266

Step-by-step explanation:

Let's solve your equation step-by-step.

3/2x−5=2/x+3

3/2x+−5=2/x+3

Multiply all terms by x and cancel:

(3/2x)(x)+−5x=2+3x

3/2 x²−5x=3x+2(Simplify both sides of the equation)

3/2 x²−5x−(3x+2)=3x+2−(3x+2)(Subtract 3x+2 from both sides)

3/2 x²−8x−2=0

For this equation: a=1.5, b=-8, c=-2

1.5x2+−8x+−2=0

x=−b±√b2−4ac (divided by) 2a (Use quadratic formula with a=1.5, b=-8, c=-2)

x= −(−8)±√(−8)2−4(1.5)(−2) (divided by) 2(1.5)

x= 8±√76 (divided by) 3

x=5.572599295693782,−0.2392659623604493

Check answers. (Plug them in to make sure they work.)

x=5.572599(Works in the original equation)

x=−0.239266(Works in the original equation)

Answer:

x=5.572599 or x=−0.239266

Answer 2

Question:

Solve for x and verify your answer.

$\large{\tt{ \frac{3}{2x-5}=\frac{2}{x+3}}}$

Answer:-

$\large{\tt{ \frac{3}{2x-5}=\frac{2}{x+3}}}$

→ $\large{\tt{3(x+3) =\: 2(2x -5) }}$ ••••( on cross multiplication)

→ $\large{\tt{ 3x + 9 = 4x - 10}}$

→ $\large{\tt{ 3x - 4x = -10 - 19}}$

→ $\large{\tt{ -x = -19}}$

→ $\large{\boxed{\tt{ x = 19 }}}$ ••••( both mines will cancel)

$\large{\boxed{\tt{\pink{ ∴\:x =\: 19}}}}$

Verification:-

We found the value of x is 19. To verify this, we have to put the value of x in equation and have to make LHS = RHS.

Verifying:-

$\large{\tt{\frac{3}{2×19-5}=\: \frac{2}{19+3}}}$

→ $\large{\tt{ \frac{3}{38-5}=\: \frac{2}{22}}}$

→ $\large{\tt{\frac{3}{33}=\: \frac{2}{22}}}$

→ $\large{\tt{ 3(22)=\: 2(33)}}$ ••••(on cross multiplication)

→ $\large{\tt{ 66 =\: 66}}$

$\large{\boxed{\tt{\pink{ LHS\: =\: RHS ~~~•••••( proved)}}}}$