Equations Step3

Equations [Step3]

To solve an equation with brackets:

(A) First, remove the brackets.

To remove the brackets, multiply all the terms in the brackets with the term outside the brackets.

(B) Then, remove the x-terms from the right side, and remove the constant terms from the left side.
(C) Finally, divide each side by the coefficient of the left side x.

Example 1.

7x−3(x−2)=2x+10 …(A) 7x−3x+6=2x+10	Remove the brackets. Multiply all the terms in the brackets with the term outside the brackets.
4x+6=2x+10 …(B) 4x−2x+6=2x−2x+10 2x+6=10 2x+6−6=10−6	Remove the x-terms from the right side, and remove the constant terms from the left side.
2x=4 …(C)	In order to get x for itself, divide each side by the coefficient of the left side x.
x=2	(Solution)

Attention:

Example 2.

−2(4+x)=3(x−6) …(A)	Remove the brackets. Multiply all the terms in the brackets with the term outside the brackets.
−8−2x=3x−18 …(B)	Move the x-terms to the left side, and move the constant terms to the right side.
−2x−3x=−18+8	Combine like terms..
−5x=−10 …(C)	In order to get x for itself, divide each side by the coefficient of the left side x.
x=2	(Solution)

Attention:

ExercisesSolve these equations for x.
(Select the correct answers. // Result -> correct:o,incorrect:x)

(1) 3(x−2)=−5(x+6)

Remove the brackets from both sides.

3x+6=−5x+30 3x+6=−5x−30
3x−6=−5x+30 3x−6=−5x−30

Move the x-terms to the left side, and move the constant terms to the right side.

8x=−36 8x=−24
−2x=−36 −2x=−24

Help

To get x for itself, divide each side by 8.

x=−32 x=−16
x=−3 x=3

Help

3x−6=−5x−30
To remove −5x from the right side, add 5x on both sides.
3x+5x−6=−5x+5x−30
8x−6=−30
To remove −6 from the left side, add 6 on both sides.
8x−6+6=−30+6
8x=−24

x=−3

(2) 3(3x−1)=−5(−2x−1)

Remove the brackets from both sides.

9x−1=−2x−6 9x−1=10x+5
9x−3=10x+5 9x−3=10x−5
9x−3=−10x+5 9x−3=−2x−6

Move the x-terms to the left side, and move the constant terms to the right side.

19x=2 −x=8
−x=2 19x=8

Help

To get x for itself, divide each side by 8.

x=−9 x=−8 x=−7
x=7 x=8 x=9

Help

9x−3=10x+5
To remove 10x from the right side, subtract 10x from both sides.
9x−10x−3=10x−10x+5
−x−3=5
To remove −3 from the left side, add 3 on both sides.
−x−3+3=5+3
−x=8

x=−8

(3) −3(2−4x)=5(2x−3)

Remove the brackets from both sides.

−6−4x=10x−3 −6−4x=10x−15
−6+12x=10x−15 −6−12x=10x−15
−6+12x=10x−3 −6−12x=10x−3

Move the x-terms to the left side, and move the constant terms to the right side.

22x=−21 22x=9
2x=−21 2x=−9

Help

To get x for itself, divide each side by 2.

x=−11 x=−7

x=− x=−

Help

−6+12x=10x−15
To remove 10x from the right side, subtract 10x from both sides.
−6+12x−10x=10x−10x−15
−6+2x=−15
To remove −6 from the left side, add 6 on both sides.
−6+6+2x=−15+6
2x=−9

x=−

(4) 2x−4(3−x)=6 Solution: x=−18 x=−9 x=−6 x=−3 x=3 x=6 x=9 x=18 Help
(5) 3x−7=2(x−4) Solution: x=−15 x=−11 x=−3 x=−1 x=1 x=3 x=− x=− Help
(6) 2(x+1)−3(x−2)=7+2x Solution: x=−3 x=1 x=3 x=4 x=10 x=− x=− x= Help