Question

solve and verify that lhs=rhs =17/x+3/2=-16​

Answer 1

Answer:

$\frac{-34}{35} = x$

Step-by-step explanation:

$\frac{17}{x} + \frac{3}{2} = -16$

Let the constants be on one side, and the variables be on the other.

Bring 3/2 to R.H.S by subtracting 3/2 from both sides.

$\frac{17}{x} = -16 -\frac{3}{2}$

Now, let us get -16 to fractional form to enable easy subtraction with 3/2.

$\frac{17}{x} = \frac{-32 - 3}{2}$

Now, cross multiplication can be done.  Multiply the diagonally opposite terms, and keep them on two sides of the equal sign.

$\frac{17}{x} = \frac{-35}{2}$

Now, to isolate , we can divide both sides of the equation by -35.

$34= -35x$

$x =\frac{-34}{35}$

To verify this result, let us put this value in the original expression.

We will have,

$\frac{17}{-34/35} + \frac{3}{2} = -16$

Now, dividing means multiplying by the number's reciprocal.

$\frac{17(35)}{-34} + \frac{3}{2} = -16$

17 can be cancelled out, leaving -2 in the denominator.

$\frac{35}{-2} + \frac{3}{2} = -16$

The negative symbol in the denominator can be appended to 35, instead of -2.

$\frac{-35}{2} + \frac{3}{2} = -16$

Now, since the denominators are the same, the LHS can be added.

$\frac{-32}{2} = -16$

We know that -16(2) = 32.

Therefore,

-16 = -16.

LHS = RHS.

The result has been verified.