Question

1)3(x-2)=x+2 2)5-2(x-1)=4-x 3)(7x+1)-(9x+3)=5 4)3,4+2y=7(y-2,3) 5)0,2(7-2y)=2,3-0,3(y-6) 6)2/3(1/3x-1/2)=4x+2 1/2

Answer 1

1

$3( x - 2) = x + 2 \\ 3x - 6 = x + 2 \\ 3x - x = 2 + 6 \\ 2x = 8 \\ x = 4$

2

$5 - 2(x - 1) = 4 - x \\ 5 - 2x + 2 = 4 - x \\ 7 - 2x = 4 - x \\ - 2x + x = 4 - 7 \\ - x = - 3 \\ x = 3$

3

$(7x + 1) - (9x + 3) = 5 \\ 7x + 1 - 9x - 3 = 5 \\ - 2x - 2 = 5 \\ - 2x = 5 + 2 \\ - 2x = 7 \\ x = - \frac{7}{2} = - 3.5$

4

$3.4 + 2y = 7(y - 2.3) \\ 3.4 + 2y = 7y - 16.1 \\ 2y - 7y = - 16.1 - 3.4 \\ - 5y = - 19.5 \\ y = 3.9$

5

$0.2(7 - 2y) = 2.3 - 0.3(y - 6) \\ 1.4 - 0.4y = 2.3 - 0.3y + 1.8 \\ 1.4 - 0.4y = 4.1 - 0.3y \\ - 0.4y + 0.3y = 4.1 - 1.4 \\ - 0.1 = 2.7 \\ y = - 27$

6

2/3*(1/3 х -1/2)=4х+2 1/2

2/9 х - 1/3 = 4х + 5/2

4х-6=72х+45

4х-72х=45+6

-68х=51

х=-3/4=-0.75

Answer 2

1) 4

2) 3

3) -3.5

4) 3.9

5) -27

6) -0.75

Answer 3

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

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

Expand the left side: $3x - 6 = x + 2$

Move all $x$ terms to one side and constants to the other side:

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

$2x = 10$

Now divide by 2 to isolate $x$:

$x = 5$

So, the solution for this equation is $x = 5$.

2. $5 - 2(x-1) = 4 - x$

Expand the left side: $5 - 2x + 2 = 4 - x$

Combine like terms: $7 - 2x = 4 - x$

Move all $x$ terms to one side and constants to the other side:

$-2x + x = 4 - 7$

$-x = -3$

Multiply both sides by -1 to isolate $x$:

$x = 3$

So, the solution for this equation is $x = 3$.

3. $(7x+1) - (9x+3) = 5$

First, perform the operation inside the parentheses:

$7x + 1 - 9x - 3 = 5$

Combine like terms:

$-2x - 2 = 5$

Move the constant term to the other side:

$-2x = 5 + 2$

$-2x = 7$

Divide both sides by -2 to find $x$:

$x = -\frac{7}{2}$

So, the solution for this equation is $x = -\frac{7}{2}$.

4. $3(4+2y) = 7(y-2.3)$

First, perform the operations inside the parentheses:

$3(4) + 3(2y) = 7y - 7(2.3)$

Simplify:

$12 + 6y = 7y - 16.1$

Move all $y$ terms to one side and constants to the other side:

$6y - 7y = -16.1 - 12$

$-y = -28.1$

Multiply both sides by -1 to find $y$:

$y = 28.1$

So, the solution for this equation is $y = 28.1$.

5. $0.2(7 - 2y) = 2.3 - 0.3(y-6)$

First, perform the operations inside the parentheses:

$0.2(7) - 0.2(2y) = 2.3 - 0.3y + 1.8$

Simplify:

$1.4 - 0.2y = 4.1 - 0.3y$

Move all $y$ terms to one side and constants to the other side:

$-0.2y + 0.3y = 4.1 - 1.4$

$0.1y = 2.7$

Divide both sides by 0.1 to find $y$:

$y = 27$

So, the solution for this equation is $y = 27$.

6. $\frac{2}{3}\left(\frac{1}{3}x - \frac{1}{2}\right) = 4x + \frac{1}{2}$

First, perform the operation inside the parentheses:

$\frac{2}{3}\left(\frac{1}{3}x - \frac{1}{2}\right) = \frac{2}{3}\left(\frac{1}{3}x\right) - \frac{2}{3}\left(\frac{1}{2}\right) = \frac{2}{9}x - \frac{1}{3}$