The value of x from the inequalities 3x – 8 < 23 and - 4x + 26 > 6 is x ≤ 5 option B
What is inequality?
An inequality is a relation that compares two numbers or other mathematical expressions in a non-equal way. The most common use case for it is size-based comparison of two integers on the number line.
Given that
3x – 8 ≤ 23
- 4x + 26 ≥ 6
From the first equation;
3x – 8 ≤ 23
3x ≤ 23 +8
3x ≤ 31
x ≤31/3
From the second equation;
- 4x + 26 ≥ 6
- 4x + 26 + 4x≥ 6 +4x
26 ≥ 6 +4x
20 ≥ 4x
5 ≥ x
x ≤ 5
Then we have x ≤ 5 and x ≤ 10.33
Now we can consider the two equation and draw a statement as
Is it equivalent to stating that x must be less than 5 if x must be both less than 5 and less than 10.33 We eliminate the requirement that x be smaller than 10.33 since it is a part of the other Hence x ≤ 5