How do you solve for x: #12/x+3/4=3/2#?

Question

Julia Adams · Accepted Answer

#x=16#

First Solution.

By inspection of the equation #12/x+3/4=3/2#

We know that #3/4+3/4=3/2#, and #12/16=3/4#. Therefore, #x=16#

Option 2.

Through algebraic method

#12/x+3/4=3/2#

Multiply both sides of the equation by #x#

#x(12/x+3/4)=(3/2)x#

#12+(3x)/4=(3x)/2#

#12=(3x)/2-(3x)/4#

#12=(6x-3x)/4#

#12=(3x)/4#

#x=(12*4)/3#

#x=16#

May God bless you all. I hope this explanation helps.

Eva Abramson · Answer

#x=16#

By multiplying each term in an equation containing fractions by the LCM of the denominators, we can eliminate the denominators.

#12/x+3/4=3/2" LCM " =color(magenta)(4x)#

#(color(magenta)(4x)xx12)/x+(color(magenta)(4x)xx3)/4=(3xxcolor(magenta)(4x))/2#

#(color(magenta)(4cancelx)xx12)/cancelx+(color(magenta)(cancel4x)xx3)/cancel4=(3xxcolor(magenta)(cancel4^2x))/cancel2color(magenta)#

#48 +3x = 6x#

#48 = 3x# #x = 16#

Eva Abramson · Answer

undefined To solve for x in the equation 12/x + 3/4 = 3/2, we can follow these steps:

1. Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is 4x.

2. Multiply each term by the common denominator to eliminate the fractions. This gives us: 12(4) + 3(x) = 3(2)(4x).

3. Simplify both sides of the equation: 48 + 3x = 24x.

4. Move all terms involving x to one side of the equation and the constant terms to the other side. This gives us: 3x - 24x = -48.

5. Combine like terms: -21x = -48.

6. Divide both sides of the equation by -21 to solve for x: x = -48 / -21.

7. Simplify the fraction: x = 16/7.

Therefore, the solution to the equation is x = 16/7.