Question

1. Which value for x makes the open sentence true?

8 + 3 • x = 22 + x2



a. 5


b. 4


c. 3


d. 2





2. Which value for x makes the sentence true?



5 + 4 • x = 32 + 2x



a. 2



b. 5


c. 3


d. 4

Answer 1

Hello!

The easiest way to find the number that makes the statement true is to substitute the given answers into the equation.

Question 1:

8 + 3 • x = 22 + x² when x = 5

8 + 3 • 5 = 22 + 5²

8 + 15 = 22 + 25

23 = 47 | x = 5 makes the equation false.

8 + 3 • x = 22 + x² when x = 4

8 + 3 • 4 = 22 + 4²

8 + 12 = 22 + 16

20 + 38 | x = 4 makes the equation false.

8 + 3 • x = 22 + x² when x = 3

8 + 3 • 3 = 22 + 3²

8 + 9 = 22 + 9

17 = 31 | x = 3 makes the equation false.

8 + 3 • x = 22 + x² when x = 2

8 + 3 • 2 = 22 + 2²

8 + 6 = 22 + 4

14 = 26 | x = 2 makes the equation false.

For question number 1, no values for x can make this equation true.

Question 2:

5 + 4 • x = 32 + 2x when x = 2

5 + 4 • 2 = 32 + 2(2)

5 + 8 = 32 + 4

13 = 36 | x = 2 makes the equation false.

5 + 4 • x = 32 + 2x when x = 5

5 + 4 • 5 = 32 + 2(5)

5 + 20 = 32 + 10

35 = 42 | x = 5 makes the equation false.

5 + 4 • x = 32 + 2x when x = 3

5 + 4 • 3 = 32 + 2(3)

5 + 12 = 32 + 6

17 = 38 | x = 3 makes the equation false.

5 + 4 • x = 32 + 2x when x = 4

5 + 4 • 4 = 32 + 2(4)

5 + 16 = 32 + 8

21 = 40 | x = 4 makes the equation false.

For question number 2, no values for x can make this equation true.

Hence, no x-values can make the equations of question one and two true.

Answer 2

1. 4

2. All my came to 27/2 or 13.5

Explanation:

1. Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

2. Can't help