Question

1) 9x − 26 = 30 − 5x; 2) x − 15 = 4 (6x − 21); 3) 4 + 8y + 8 = 2y − (10 + 7y) + 9; 4) 6 (12x − 5) − 13x = 59x − 30; 5) 5 − 3 (z + 5) = 7 − (2 + 3z); 6) 5 (x − 3) − 2 (x − 7) = 7 − 7 (2x + 6); 7) 28 − 20x = 2x + 25 − 16x − 12 − 6x; 8) 10 − 4x + 3 = 9x − 2 − 6x + 9 − 7x + 6.

Answer 1

9х-26=30-5х
9х+5х=56
14х=56
х=4

х-15=4(6х-21)
х-15=24х-84
23х=69
х=3


4+8у+8=2у-(10+7у)+9
8у-2у-7у=-4-8-10+9
-1у=-22+9
-1у = - 13
1у=13

10-4х+3=9х-2-6х+9-7х+6
-4х+13=-4х+13
0=0


6(12х-5)-13х=59х-30
72х-30-13х=59х-30
59х-30=59х-30
0=0

Answer 2

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

1. 9x - 26 = 30 - 5x

First, let's get all the x terms on one side and the constant terms on the other side:

9x + 5x = 30 + 26

Combine like terms:

14x = 56

Now, divide both sides by 14 to solve for x:

x = 56 / 14 x = 4

2. x - 15 = 4(6x - 21)

Distribute the 4 on the right side of the equation:

x - 15 = 24x - 84

Now, get the x terms on one side and the constant terms on the other side:

x - 24x = -84 + 15

Combine like terms:

-23x = -69

Now, divide both sides by -23 to solve for x:

x = -69 / -23 x = 3

3. 4 + 8y + 8 = 2y - (10 + 7y) + 9

First, simplify the expression within the parentheses:

4 + 8y + 8 = 2y - 10 - 7y + 9

Combine like terms on both sides:

12y + 12 = -5y - 1

Now, get the y terms on one side and the constant terms on the other side:

12y + 5y = -1 - 12

Combine like terms:

17y = -13

Now, divide both sides by 17 to solve for y:

y = -13 / 17

4. 6(12x - 5) - 13x = 59x - 30

First, distribute the 6 on the left side of the equation:

72x - 30 - 13x = 59x - 30

Now, get the x terms on one side and the constant terms on the other side:

72x - 13x - 59x = 30 - 30

Combine like terms:

-4x = 0

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

x = 0

5. 5 - 3(z + 5) = 7 - (2 + 3z)

First, distribute the -3 and -1 on both sides of the equation:

5 - 3z - 15 = 7 - 2 - 3z

Combine like terms:

-3z - 10 = 5 - 3z

Now, notice that the variable terms (-3z) cancel out on both sides. This means that there are infinitely many solutions, and the equation is dependent on the value of z.

6. 5(x - 3) - 2(x - 7) = 7 - 7(2x + 6)

First, distribute the numbers on both sides of the equation:

5x - 15 - 2x + 14 = 7 - 14x - 42

Now, combine like terms:

3x - 1 = 7 - 14x - 42

Combine like terms on both sides:

3x + 14x = 7 - 42 + 1

17x = -34

Now, divide both sides by 17 to solve for x:

x = -34 / 17 x = -2

7. 28 - 20x = 2x + 25 - 16x - 12 - 6x

First, combine like terms on the right side of the equation:

28 - 20x = 2x + 25 - 16x - 12 - 6x

Now, simplify the right side further:

28 - 20x = 2x - 16x - 6x + 25 - 12

Combine like terms on the right side:

28 - 20x = -20x + 13

Now, notice that the variable terms (-20x) cancel out on both sides. This means that there are infinitely many solutions, and the equation is dependent on the value of x.

8. 10 - 4x + 3 = 9x - 2 - 6x + 9 - 7x + 6

First, combine like terms on both sides:

10 - 4x + 3 = 9x - 2 - 6x + 9 - 7x + 6

Now, simplify each side:

10 - 4x + 3 = 9x - 2 - 6x + 9 - 7x + 6

Combine like terms on both sides:

10 - 4x + 3 = -4x

Now, notice that the variable terms (-4x) cancel out on both sides. This means that there are infinitely many solutions, and the equation is dependent on the value of x.