Math help, please? Algebra II?

Question

Solve.
1. 11(z - 5) = 2(z - 6) - 13

Solve the inequality. Then graph the solution.
2. -9 ≤ 5 - 2x < 7

Graph the inequality in a coordinate plane
3. x + 2y > 8

Solve the system using any algebraic method.
4. 3x + 2y = 4
-7x - 5y = -7

Answer 1

1). 11(z - 5) = 2(z - 6) - 13

Distribute terms using distributive property:  a( b + c) = ab + ac

11(z) - 11(5) = 2(z) - 2(6) - 13

11z - 55 = 2z - 12 - 13

11z - 55 = 2z - 25

Subtract 2z from each side.

11z - 2z - 55 = 2z - 25 - 2z

9z - 55 = - 25

Add 55 to each side.

9z - 55 + 55 = - 25 + 55

9z = 30

Divide each side by 9.

9z/9 = 30/9

z = 10/3.

Answer 2

2). - 9 ≤ 5 - 2x < 7

- 9 ≤ 5 - 2x or 5 - 2x < 7

Take - 9 ≤ 5 - 2x

Subtract 5 from each side.

- 14 ≤ - 2x

Multiply each side by negative one and flip the symbol.

14 ≥ 2x

Divide each side by 2.

7 ≥ x

And take 5 - 2x < 7

Subtract 5 from each side.

- 2x < 2

Divide each side by 2.

-x < 1

Multiply each side by negative one and flip the symbol.

x > -1.

Therefore x ≤ 7 or x > -1.

Graph the solution set on a number line.

Answer 3

4.  3x + 2y = 4------------>(1)

 -7x - 5y = -7------------>(2)

Multiply equation (1) by 5, Multiply equation (2) by 2 and solving equation (1) and equation (2)

15x + 10y = 20

-14x - 10y = -14

----------------------------

x = 6

Substituting x = 6 in the equation (1)

3(6) + 2y = 4.

18 + 2y = 4

Subtract 18 from each side.

2y = - 14

Divide each side by 2.

y = -7

Therefore (x, y) = (6, -7)

Answer 4

3) The inequality  x + 2y > 8

x + 2y > 8

Related equation is x + 2y = 8

2y = -x + 8

y = -x/2 + 4

Draw the coordinate plane.

Step 1:

To graph the inequality x + 2y > 8, first graph the line y = -x/2 + 4.

Since x + 2y > 8, The graph of y = -x/2 + 4 is dashed and is not included in the graph of x + 2y > 8.

Then shade region above the line.

Step 2:

To know the which section to be shaded use a test point like (0, 0).

Substitute and x = 0 and y = 0 in original inequality x + y ≤ 8

0 + 2 (0) > 8 ----> 0 > 8

The statement is false.

Since the statement is false, Shade the region ecxcept that contains the point (0, 0).