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

Answer 1

#x=5#

#(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#

Resolving the left side:

#= (5-3)/4+5/2#
#= 2/4+5/2#
#=1/2+5/2#
#=(1+5)/2#
#=6/2=color(red)(3)#
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Answer 2

x = 5

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#

Now that the equation is simplified, it becomes

x - 3 + 2x = 12.

Consequently, 3x - 3 = 12.

and 3x equals 15

divide each side by three.

#(cancel(3)^1 x)/cancel(3)^1 =15/3#
#rArrx=5" is the solution"#
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Answer 3

To solve the equation (x-3)/4 + x/2 = 3, you can follow these steps:

  1. Multiply every term in the equation by the common denominator, which is 4. This will eliminate the fractions. (x-3)/4 * 4 + x/2 * 4 = 3 * 4

  2. Simplify the equation by canceling out terms and distributing. (x-3) + 2x = 12

  3. Combine like terms by adding the x terms and the constant terms separately. x - 3 + 2x = 12 3x - 3 = 12

  4. Isolate the variable by moving the constant term to the other side of the equation. 3x = 12 + 3 3x = 15

  5. Solve for x by dividing both sides of the equation by the coefficient of x. x = 15/3

  6. Simplify the result. x = 5

Therefore, the solution to the equation (x-3)/4 + x/2 = 3 is x = 5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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