Question

0.1) 5(x - 1) + 7 = 3(x + 1) + 1; 3) 3(3x + 5) - 4(3x - 5) = 0; 2) 2(x + 1) + 3 = 3(x - 1) + 6; 4) 7(5-X) + 2 = 5(6 - X) + 1.​

Answer 1

1) x=1 3) x=35/3

2) x=1 4) x=3

Answer 2

Let's solve each of these equations step by step:

1. 5(x - 1) + 7 = 3(x + 1) + 1

First, distribute the constants inside the parentheses:

5x - 5 + 7 = 3x + 3 + 1

Now, combine like terms on both sides of the equation:

5x + 2 = 3x + 4

Subtract 3x from both sides:

2x + 2 = 4

Subtract 2 from both sides:

2x = 2

Now, divide both sides by 2 to solve for x:

x = 1

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

First, distribute the constants inside the parentheses:

2x + 2 + 3 = 3x - 3 + 6

Now, combine like terms on both sides of the equation:

2x + 5 = 3x + 3

Subtract 3x from both sides:

2x - 3x + 5 = 3

Now, subtract 5 from both sides:

-1x = -2

Divide both sides by -1 to solve for x:

x = 2

3. 3(3x + 5) - 4(3x - 5) = 0

First, distribute the constants inside the parentheses:

9x + 15 - 12x + 20 = 0

Combine like terms on both sides of the equation:

(9x - 12x) + (15 + 20) = 0

-3x + 35 = 0

Subtract 35 from both sides:

-3x = -35

Now, divide both sides by -3 to solve for x:

x = 35 / 3

4. 7(5 - x) + 2 = 5(6 - x) + 1

First, distribute the constants inside the parentheses:

35 - 7x + 2 = 30 - 5x + 1

Combine like terms on both sides of the equation:

35 - 7x + 2 = 30 - 5x + 1

Now, combine like terms:

-7x + 37 = -5x + 31

Subtract -5x from both sides:

-7x + 37 + 5x = 31

Combine like terms:

-2x + 37 = 31

Subtract 37 from both sides:

-2x = 31 - 37

-2x = -6

Divide both sides by -2 to solve for x:

x = 3