How do you solve (x-3) /4 + x/2 =3?

2 Answers
Jun 3, 2016

x=5

Explanation:

(x-3)/4+x/2=3

First, we remove the fractions by multiplying the equation by the LCM of 4 and 2, our two denominators:

LCM of 4 and 2 = 4

Multiply the equation by 4.

This means, the expression on the left side of the = sign will be multiplied by 4 and the expression on the right side of the = sign will be multiplied by 4:

[(x-3)/4+x/2]color(red)(xx4)=3color(red)(xx4)

[(x-3)/4color(red)(xx4)]+[x/2color(red)(xx4)]=12

[(x-3)/cancel4xxcancel 4]+[x/cancel2xxcancel4^2]=12

x-3+(x xx2)=12

x-3+2x=12

3x-3=12

Next, add 3 to both sides of the equation:

3x-3color(red)(+3)=12color(red)(+3)

3x=15

Finally, divide both sides by 3:

(3x)/color(red)(3)=15/color(red)(3)

x=5

You can check your answer by putting back the value x=5 in the question:

(x-3)/4+x/2=3

Solving the left side:

= (5-3)/4+5/2

= 2/4+5/2

=1/2+5/2

=(1+5)/2

=6/2=color(red)(3)

Jun 3, 2016

x = 5

Explanation:

To eliminate the fractions in this equation color(blue)"multiply all terms on both sides" by the L.C.M. (lowest common multiple) of 2 and 4 which is 4.

rArr[cancel(4)^1 xx(x-3)/cancel(4)^1]+[cancel(4)^2xxx/cancel(2)^1]=4xx3

The equation now simplifies to

x - 3 + 2x = 12

hence : 3x - 3 =12

and 3x = 15

divide both sides by 3

(cancel(3)^1 x)/cancel(3)^1 =15/3

rArrx=5" is the solution"