Question

−15x+4≤109 OR −6x+70>−2minus, 15, x, plus, 4, is less than or equal to, 109, start color #ed5fa6, start text, space, O, R, space, end text, end color #ed5fa6, minus, 6, x, plus, 70, is greater than, minus, 2 Choose 1 answer: Choose 1 answer:

(Choice A) A x\geq-7x≥−7x, is greater than or equal to, minus, 7.
(Choice B) B -7\leq x<12−7≤x<12minus, 7, is less than or equal to, x, is less than, 12.
(Choice C) C x<12x<12x, is less than, 12.
(Choice D) D There are no solutions .
(Choice E) E All values of xxx are solutions.

Answer 1

Hi There Answer Choice E

Explanation:

−15x+4≤109 OR −6x+70>−2minus, 15, x, plus, 4, is less than or equal to, 109, start color #ed5fa6, start text, space, O, R, space, end text, end color #ed5fa6, minus, 6, x, plus, 70, is greater than, minus, 2 Choose 1 answer: Choose 1 answer:

(Choice A) A x\geq-7x≥−7x, is greater than or equal to, minus, 7.

(Choice B) B -7\leq x<12−7≤x<12minus, 7, is less than or equal to, x, is less than, 12.

(Choice C) C x<12x<12x, is less than, 12.

(Choice D) D There are no solutions .

(Choice E) E All values of xxx are solutions.

Answer 2

Option E.

Explanation:

The given inequalities are

`-15x+4\leq 109`

`-6x+70>-2`

We need to find the solution of given compound inequality.

Solve each inequality separately.

Solve first inequality:

`-15x+4\leq 109`

Subtract 4 from both sides.

`-15x\leq 109-4`

`-15x\leq 105`

Divide both sides by -15. If we multiply or divide an inequality by a negative number, then the sign of inequality is changed.

`x\geq -7` .... (1)

Solve second inequality:

`-6x+70>-2`

Subtract 70 from both sides.

`-6x>-2-70`

`-6x>-72`

Divide both sides by -6.

`x<12` .... (2)

Form (1) and (2) we get

`x\geq -7\text{ or }x<12=\text{All real numbers}`

Therefore, the correct option is E.