Examkin

Question

Difficulty: MediumSolving One-Variable Inequalities

The value x=2x = 2 is a valid solution for the inequality 5−2(3x+1)<4x−175 - 2(3x + 1) < 4x - 17.

Answer: Answer

Answer

False
Substituting x=2x = 2 into both sides of the inequality results in −9<−9-9 < -9. Because −9-9 is equal to −9-9 and not strictly less than it, the mathematical statement is false. Alternatively, fully solving the inequality yields x>2x > 2, which does not include 22 as a solution.

Step-by-Step Solution

1
Substitute x=2x = 2 into the left side of the inequality.
5−2(3(2)+1)=5−2(6+1)=5−2(7)=5−14=−95 - 2(3(2) + 1) = 5 - 2(6 + 1) = 5 - 2(7) = 5 - 14 = -9
To evaluate the numerical value of the left expression for the given test value.
2
Substitute x=2x = 2 into the right side of the inequality.
4(2)−17=8−17=−94(2) - 17 = 8 - 17 = -9
To evaluate the numerical value of the right expression for the given test value.
3
Compare the two evaluated sides using the strict inequality symbol (<<).
−9<−9-9 < -9
To determine if the resulting mathematical relationship is true.
4
Evaluate the truth of the final statement.
Since −9-9 is exactly equal to −9-9, it is not strictly less than −9-9. The statement is therefore false.
A strict inequality requires the left side value to be genuinely smaller than the right side value.

Key Concept

Solving One-Variable Inequalities
Rate this question

Topics

Solving One-Variable Inequalities

More questions from this topic