Respuesta :
Given:
The inequalities are:
1. [tex]x-85.2\leq 14.6[/tex]
2. [tex]\dfrac{x}{6}>-23[/tex]
3. [tex]x-43<37[/tex]
4. [tex]8x\leq 128[/tex]
5. [tex]x+4.7>21.6[/tex]
To find:
The inequalities that have 4 as a solution.
Solution:
We need to put [tex]x=4[/tex] in each inequality, to check whether it is a solution or not.
1. The inequality is
[tex]x-85.2\leq 14.6[/tex]
Putting [tex]x=4[/tex], we get
[tex]4-85.2\leq 14.6[/tex]
[tex]-81.2\leq 14.6[/tex]
This statement is true. So, the inequality [tex]x-85.2\leq 14.6[/tex] has 4 as a solution.
2. The inequality is
[tex]\dfrac{x}{6}>-23[/tex]
Putting [tex]x=4[/tex], we get
[tex]\dfrac{4}{6}>-23[/tex]
[tex]0.67\leq -23[/tex]
This statement is true. So, the inequality [tex]\dfrac{x}{6}>-23[/tex] has 4 as a solution.
3. The inequality is
[tex]x-43<37[/tex]
Putting [tex]x=4[/tex], we get
[tex]4-43<37[/tex]
[tex]-39<37[/tex]
This statement is true. So, the inequality [tex]x-43<37[/tex] has 4 as a solution.
4. The inequality is
[tex]8x\leq 128[/tex]
Putting [tex]x=4[/tex], we get
[tex]8(4)\leq 128[/tex]
[tex]32\leq 128[/tex]
This statement is true. So, the inequality [tex]8x\leq 128[/tex] has 4 as a solution.
5. The inequality is
[tex]x+4.7>21.6[/tex]
Putting [tex]x=4[/tex], we get
[tex]4+4.7>21.6[/tex]
[tex]8.7>21.6[/tex]
This statement is false. So,4 is not a solution of the inequality [tex]x+4.7>21.6[/tex].
