In this question we have eight expressions involving <em>absolute value</em> expressions, which can be solved by using the following procedure:

3.1 a) |(1 / 2) · x| = 3 - 2 · x

For x ≥ 0:

(1 / 2) · x = 3 - 2 · x

(5 / 2) · x = 3

x = 6 / 5

For x < 0:

- (1 / 2) · x = 3 - 2 · x

(3 / 2) · x = 3

x = 2

b) |x - 1| = 3 · x + 2

For x ≥ 1:

x - 1 = 3 · x + 2

2 · x = - 3

x = - 3 / 2

For x < 1:

- x + 1 = 3 · x + 2

4 · x = - 1

x = - 1 / 4

c) |5 · x| = x - 12

For x ≥ 0:

5 · x = x - 12

4 · x = - 12

x = - 3

For x < 0:

- 5 · x = x - 12

6 · x = 12

x = 2

d) |7 - x| = 5 · x + 1

For x ≤ 7:

7 - x = 5 · x + 1

6 · x = 6

x = 1

For x > 7:

x - 7 = 5 · x + 1

4 · x = - 8

x = - 2

3.2 a) |9 + x| = 2 · x

For x ≥ - 9:

9 + x = 2 · x

x = 9

For x < 9:

- 9 - x = 2 · x

3 · x = - 9

x = - 3

b) |5 · x| - 3 · x = 2

For x ≥ 0:

|5 · x| = 2 + 3 · x

5 · x = 2 + 3 · x

2 · x = 2

x = 1

For x < 0:

- 5 · x = 2 + 3 · x

- 8 · x = 2

x = - 1 / 4

c) |x + 6| - 9 = 2 · x

For x ≥ - 6:

x + 6 - 9 = 2 · x

x - 3 = 2 · x

x = - 3

For x < - 6:

- x - 6 - 9 = 2 · x

- x - 15 = 2 · x

3 · x = - 15

x = - 5

d) |2 · x - 3| + x = 21

For x ≥ 3 / 2:

2 · x - 3 + x = 21

3 · x = 24

x = 8

For x < 3 / 2:

- 2 · x + 3 + x = 21

- x = 18

x = - 18

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3 0

2 years ago

Evaluate the following expression using the values given:

Rom4ik [11]

The answer to this question is 35

4 0

2 years ago

If ∠ABE = 100° and ∠EDC = 100°, are the two triangles, ΔABE and ΔEDC similar? If so, by what criterion?

Arturiano [62]

Answer:

No, not possible to tell that the two triangles, ΔABE and ΔEDC are similar

Step-by-step explanation:

Similarity criterion:

1. AAA similarity : two triangles are similar if all three angles in the first

triangle equal the corresponding angle in the second triangle

2. AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.

3. SSS similarity : If the corresponding sides of the two triangles are

proportional, then the two triangles are similar.

4. SAS similarity : In two triangles, if two sets of corresponding sides

are proportional and the included angles are equal then the two

triangles are similar.

Now in the two triangles ABE and EDC :

∠ABE = 100°

∠EDC = 100°

∠ABE = ∠EDC

But only one congruent angle does not not prove that the two triangles are similar.

Hence, NOTHING CAN BE SAID ABOUT THE nature of the triangle.

3 0

2 years ago

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