1) 1/3(x+3)+1/6=1/2(x-1)-(x-3)

x= 8/5

Step-by-step explanation:

Let's solve your equation step-by-step.

1

3

(x+3)+

1

6

=

1

2

(x−1)−(x−3)

Step 1: Simplify both sides of the equation.

1

3

(x+3)+

1

6

=

1

2

(x−1)−(x−3)

1

3

(x+3)+

1

6

=

1

2

(x−1)+−1(x−3)(Distribute the Negative Sign)

1

3

(x+3)+

1

6

=

1

2

(x−1)+−1x+(−1)(−3)

1

3

(x+3)+

1

6

=

1

2

(x−1)+−x+3

(

1

3

)(x)+(

1

3

)(3)+

1

6

=(

1

2

)(x)+(

1

2

)(−1)+−x+3(Distribute)

1

3

x+1+

1

6

=

1

2

x+

−1

2

+−x+3

(

1

3

x)+(1+

1

6

)=(

1

2

x+−x)+(

−1

2

+3)(Combine Like Terms)

1

3

x+

7

6

=

−1

2

x+

5

2

1

3

x+

7

6

=

−1

2

x+

5

2

Step 2: Add 1/2x to both sides.

1

3

x+

7

6

+

1

2

x=

−1

2

x+

5

2

+

1

2

x

5

6

x+

7

6

=

5

2

Step 3: Subtract 7/6 from both sides.

5

6

x+

7

6

−

7

6

=

5

2

−

7

6

5

6

x=

4

3

Step 4: Multiply both sides by 6/5.

(

6

5

)*(

5

6

x)=(

6

5

)*(

4

3

)

x=

8

5

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step-by-step explanation: