Question

An equation is shown below:
3/2x + 7/2 = 2^x

X = 1

X = 3

X = 5

X = 8

Answer 1

x=3 because
$\frac{3}{2} \times 3 = \frac{9}{2}$
$\frac{9}{2} + \frac{7}{2} = 8$
And
${2}^{3} = 8$
So the equation is balanced

Answer 2

Answer:

Option - 2, The solution of the equation is at x=3.

Step-by-step explanation:

Given : Equation $\frac{3}{2}x+\frac{7}{2}=2^x$

To find : The point which satisfy the equation?

Solution :

To find the point we put all the given points one by one which satisfy the equation is the required point.

$\frac{3}{2}x+\frac{7}{2}=2^x$

1) Put x=1,

$\frac{3}{2}(1)+\frac{7}{2}=2^1$

$\frac{3+7}{2}=2$

$\frac{10}{2}=2$

$5\neq2$

x=1 is not a point.

2) Put x=3,

$\frac{3}{2}(3)+\frac{7}{2}=2^3$

$\frac{9+7}{2}=8$

$\frac{16}{2}=8$

$8=8$

x=3 is a point satisfying equation.

3) Put x=5,

$\frac{3}{2}(5)+\frac{7}{2}=2^5$

$\frac{15+7}{2}=32$

$\frac{22}{2}=32$

$11\neq32$

x=5 is not a point.

4) Put x=8,

$\frac{3}{2}(8)+\frac{7}{2}=2^8$

$\frac{24+7}{2}=256$

$\frac{31}{2}=256$

$15.5\neq256$

x=8 is not a point.

Therefore, The solution of the equation is at x=3.