Question

8. 1) 7x - (3 + 2x) = x + 9; 2) 13 - (2x - 5) = x - 3;3) 3x - (10 - 9x)= 22x;4) 26 - (17 - 2x) = 5x​

Answer 1

$1) 7x-(3+2x)=x+9$

$7x-3-2x=x+9$

$5x-3=x+9$

$5x-x=3+9$

$4x=12$

$x=3$

$2) 13-(2x-5)=x-3$

$13-2x+5=x-3$

$18-2x=x-3$

$-x-2=-18-3$

$-3x=-21$

$x=7$

$3) 3x-(10-9x)=22x$

$3x-10+9x=22x$

$12x-10=22x$

$12x-22x=10$

$-10x=10$

$x=-1$

$4) 26-(17-2x)=5x$

$26-17+2x=5x$

$9+2x=5x$

$-5x+2x=-9$

$-3x=-9$

$x=3$

Answer 2

To solve these equations, you'll need to simplify and isolate the variable x. Let's solve each equation step by step:

1. 7x - (3 + 2x) = x + 9

First, distribute the negative sign inside the parentheses:

7x - 3 - 2x = x + 9

Now, combine like terms by subtracting 2x from both sides of the equation:

7x - 2x - 3 = x + 9 - 2x

This simplifies to:

5x - 3 = x + 9 - 2x

Now, isolate x by adding 3 to both sides of the equation:

5x - 3 + 3 = x + 9 - 2x + 3

5x = x + 12

Next, subtract x from both sides:

5x - x = x - x + 12

4x = 12

Now, divide both sides by 4 to solve for x:

4x/4 = 12/4

x = 3

So, the solution to the first equation is x = 3.

2. 13 - (2x - 5) = x - 3

First, distribute the negative sign inside the parentheses:

13 - 2x + 5 = x - 3

Combine like terms by adding 2x to both sides:

13 - 2x + 2x + 5 = x - 3 + 2x

This simplifies to:

18 = 3x - 3

Now, add 3 to both sides of the equation:

18 + 3 = 3x - 3 + 3

21 = 3x

Next, divide both sides by 3 to solve for x:

21/3 = 3x/3

7 = x

So, the solution to the second equation is x = 7.

3. 3x - (10 - 9x) = 22x

First, distribute the negative sign inside the parentheses:

3x - 10 + 9x = 22x

Combine like terms by adding 10 to both sides:

3x + 9x - 10 + 10 = 22x + 10

This simplifies to:

12x = 22x + 10

Now, subtract 22x from both sides of the equation:

12x - 22x = 22x - 22x + 10

-10x = 10

Next, divide both sides by -10 to solve for x:

(-10x)/(-10) = 10/(-10)

x = -1

So, the solution to the third equation is x = -1.

4. 26 - (17 - 2x) = 5x

First, distribute the negative sign inside the parentheses:

26 - 17 + 2x = 5x

Combine like terms by adding 17 to both sides:

26 - 17 + 17 + 2x = 5x + 17

This simplifies to:

9 + 2x = 5x + 17

Now, subtract 2x from both sides of the equation:

9 + 2x - 2x = 5x - 2x + 17

9 = 3x + 17

Next, subtract 17 from both sides:

9 - 17 = 3x + 17 - 17

-8 = 3x

Finally, divide both sides by 3 to solve for x:

(-8)/3 = (3x)/3

x = -8/3

So, the solution to the fourth equation is x = -8/3.