Solve 2( x-2 ) - 3( 5-x ) = 4( 2x + 1 )

Question

please solve the problem and give me the answer and the method

Answer 1

Though I cannot give the answer, I can show you how to arrive to the answer.

First, think "PEMDAS": parentheses, exponents, multiplication, division, addition, and subtraction.

Since you cannot solve the addition within the parentheses (due to not knowing "x"), you can go to the multiplication step and distribute the constants as shown:

2(x-2)-3(5-x) = 4(2x+1)

2x-4-15+3x= 8x+4

 

Now "combine like terms" (x's with x's and numbers with numbers) using addition and subtraction:

5x-19=8x+4

Now, you need to move the numbers on to one side and the x's to the other. You can do this by "doing the opposite" of what the equation tells you to do. In this case, one side (the right hand side) says 4 is being added- do the opposite and subtract by 4 so the 4 cancels, like this:

5x-19-4=8x+4-4

5x-23= 8x

Do the same to the x's.

-23=3x

The right hand side of the equation says to multiply 3 by x, so divide by 3 to cancel the 3's and bring it to the left-hand side. You have arrived to your answer!

Message me if you have further questions.

Answer 2

2(x-2) - 3(5-x) = 4(2x+1)

 

expanding the brackets by multiplying by the numbers outside;

 

2x - 4 - 15 +3x = 8x +4 (remember that unlike signs multiplying gives a negative, and like signs give a positive)

 

subtracting 8x from both sides; 2x - 4 - 15 + 3x - 8x = 4x + 4 - 4x = (2x + 3x - 8x) - 4 - 15 = 4

 

adding 4 + 15 to both sides; -3x -4 -15 + 4 + 15 = 4 + 4 + 15

 

-3x = 23; or x = -7 2/3 or -7.67

 

checking; 2(-9.67) -3(12.67) = 4(-15.33 + 1)

 

         -57.33 = -57.33 (proven)