Question

Which of the following pairs of inequalities are equivalent

x-5> 4 and 2x-10 >8

x- 5 >4 and 2x +10 >8

x+5 >4 and 2x+10 <8

ALL​

Answer 1

Answer:

(a): $x-5> 4$ and $2x-10 >8$

Step-by-step explanation:

Given

Pairs of inequalities

Required

Select which is equivalent

(a): $x-5> 4$ and $2x-10 >8$

Multiply both sides of $x-5> 4$ by 2

$2 * (x - 5) > 4 *2$

$2 * x - 2*5 > 4 *2$

$2x - 10 > 8$

Hence: $x-5> 4$ is equivalent to $2x - 10 > 8$

(b): $x-5> 4$ and $2x+10 >8$

Multiply both sides of $x-5> 4$ by 2

$2 * (x - 5) > 4 *2$

$2 * x - 2*5 > 4 *2$

$2x - 10 > 8$

Hence: $x-5> 4$ is not equivalent to $2x+10 <8$

(c): $x+5> 4$ and $2x+10 <8$

Multiply both sides of $x+5> 4$ by 2

$2 * (x + 5) > 4 *2$

$2 * x + 2*5 > 4 *2$

$2x + 10 > 8$

Hence: $x+5> 4$ is not equivalent to $2x+10 <8$