Equations [Step2]
To solve an equation:
If an equation involves several x-terms or several constant terms, move the x-terms to the left side, and move the constant terms to the right side of the equation.
Finally, divide each side by the coefficient of the left side x.
Example 1.
7x+2=4x+8 In order to remove 4x from the right side, subtract 4x from both sides.
7x−4x+2=4x−4x+8 …(A) In the left side,
7x−4x=(7−4)x=3x.
In the right side, 4x−4x=0.
3x+2=8 In order to remove 2 from the left side, subtract 2 from both sides.
3x+2−2=8−2 …(B) In the left side: +2−2=0.
In the right side: 8−2=6.
3x=6 …(C) In order to get x for itself, divide each side by 3.
x=2 (Solution)
Example 2.
−4x−3=−x+9 In order to remove −x from the right side, add x on both sides.
−4x+x−3=−x+x+9 …(A) In the left side,
−4x+x=(−4+1)x=−3x.
In the right side, −x+x=0.
−3x−3=9 In order to remove −3 from the left side, add 3 on both sides.
−3x−3+3=9+3 …(B) In the left side, −3+3=0.
In the rright side, 9+3=12.
−3x=12 …(C) In order to get x for itself, divide each side by −3.
x=−4 (Solution)


Notice
You can use only addition or subtraction in step (A),(B).
You can use division only in step (C).

Common mistakes
4x in the right side never mean 4x in the left side.
7x+2=4x+8 -> 7x+4x+2=8 x
You can add or subtract only terms.You should not add or subtract the coefficient of the variable.
7x+2=4x+8 -> 7x+2−4=8 x
3x=6 -> x=6−3 x
ExercisesSolve these equations for x.
(Select the correct answers. // Result -> correct:o,incorrect:x)
(1) 5x+3=2x+15
To remove 2x from the right side, subtract 2x from both sides.
?x+3=15
(2) x+5=−3x+25
To remove −3x from the right side, add 3x to both sides.
?x+5=25
(3) −4−7x=−5x+8
To remove −5x from the right side, add 5x to both sides.
?x−4=8
(4) 8−x=2x−7
To remove 2x from the right side, subtract 2x from both sides.
?x+8=−7
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