Question

How do you solve −6x+14<−28 AND3x+28≤25minus, 6, x, plus, 14, is less than, minus, 28, start color #ed5fa6, start text, space, A, N, D, end text, end color #ed5fa6, 3, x, plus, 28, is less than or equal to, 25

Choose 1 answer: Choose 1 answer: (Choice A)
A x\leq-1x≤−1x, is less than or equal to, minus, 1 or x>7x>7x, is greater than.
B -1\leq x<7−1≤x<7minus, 1, is less than or equal to, x, is less than.
C x<7x<7x, is less than.
D There are no solutions.
E All values of xxx are solutions.

Answer 1

Answer: D) there are no solutions

Explanation:

Answer 2

Answer: D There are no solutions.

Explanation:

First you must note that we solve inequalities just like normal equation, the only difference is that the sign of inequality will change whenever we multiply both sides by a minus sign or reciprocate both sides.

To solve -6x+14<-28

Subtract 14 from both sides,

= -6x+14-14<-28-14

= -6x<-42

Multiplying both sides by minus we have;

= 6x>42 (Note that the sign changed to greater than)

Dividing both sides by 6, we have

x>7 or 7<x....(1)

Similarly for 3x+28≤25

Subtracting 28 from both sides we have;

3x+28-28≤25-28

3x≤-3

x≤-1...(2)

Combining (1) and (2) inequalities, we have 7<x≤-1

Therefore, there are no solutions