Question

Which value for x makes the open sentence true?

Answer 1

9. 4- 2(8) = -12
    55-40 = 15 
so C is true
 8. B
  
3 and 6 i dont know . seems : 4 . C & D are both correct 
                                                 6 . All correct

Answer 2

we know that

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

so

Part 1)

$4.3-2x < x^{2} -2$

a) For $x=0$

$4.3-2*0 < 0^{2} -2$

$12 < -2$ -----> is false

b) For $x=1$

$4.3-2*1 < 1^{2} -2$

$10 < -1$ -----> is false

c) For $x=2$

$4.3-2*2 < 2^{2} -2$

$8 < 2$ -----> is false

d) For $x=3$

$4.3-2*3 < 3^{2} -2$

$6 < 7$ -----> is true

therefore

the answer part 1) is the option D

$x=3$

Part 2)

$6*7-5x+x^{2} \geq x^{3} +x^{2}$

a) For $x=5$

$6*7-5*5+5^{2} \geq 5^{3} +5^{2}$

$42 \geq 150$ ----> is false

b) For $x=6$

$6*7-5*6+6^{2} \geq 6^{3} +6^{2}$

$48 \geq 252$ ----> is false

c) For $x=4$

$6*7-5*4+4^{2} \geq 4^{3} +4^{2}$

$38 \geq 80$ ----> is false

d) For $x=3$

$6*7-5*3+3^{2} \geq 3^{3} +3^{2}$

$36 \geq 36$ ----> is True

therefore

the answer Part 2) is the option D

$x=3$

Part 3)

we have

$8*3-4x\ (\ )\ 7*(10-x)$

For $x=3$

$8*3-4*3\ (\ )\ 7*(10-3)$

$12\ (\ )\ 49$

we know that

$12 < 49$

therefore

the answer Part 3)  is the option B

Part 4)

we have

$9*4-2x\ (\ )\ 5*(11-x)$

For $x=8$

$9*4-2*8\ (\ )\ 5*(11-8)$

$20\ (\ )\ 15$

we know that

$20 > 15$

therefore

the answer Part 4)  is the option B

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