Answer:
no solutions
Step-by-step explanation:
To solve the inequality [tex]0.54 |2x - 14.3| + 7.96 \leq 3.1[/tex], we can follow these steps:
Subtract 7.96 from both sides of the inequality:
[tex] 0.54 |2x - 14.3| \leq 3.1 - 7.96 [/tex]
Simplify the right side:
[tex] 0.54 |2x - 14.3| \leq -4.86 [/tex]
Divide both sides by 0.54. Note that since 0.54 is positive, the direction of the inequality does not change:
[tex] |2x - 14.3| \leq \dfrac{-4.86}{0.54} [/tex]
Simplify the right side:
[tex] |2x - 14.3| \leq -9 [/tex]
3. The inequality [tex]|2x - 14.3| \leq -9[/tex] has no solutions because an absolute value cannot be less than or equal to a negative number.
Therefore, the original inequality [tex]0.54 |2x - 14.3| + 7.96 \leq 3.1[/tex] has no solutions either.
