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Difficulty: MediumSolving One-Variable Inequalities

The value x=−2x = -2 is a valid solution to the inequality −4(x−3)≤2x+18-4(x - 3) \leq 2x + 18.

Answer: Answer

Answer

False
The statement is false because substituting −2-2 into the inequality results in 20≤1420 \leq 14, which is not mathematically accurate. Alternatively, algebraic solving yields x≥−1x \geq -1, and −2-2 does not satisfy this condition.

Step-by-Step Solution

1
Substitute x=−2x = -2 into the left side of the inequality.
−4(−2−3)=−4(−5)=20-4(-2 - 3) = -4(-5) = 20
To determine the numerical value of the left expression when x=−2x = -2.
2
Substitute x=−2x = -2 into the right side of the inequality.
2(−2)+18=−4+18=142(-2) + 18 = -4 + 18 = 14
To determine the numerical value of the right expression when x=−2x = -2.
3
Compare the two results using the given inequality symbol.
The statement 20≤1420 \leq 14 is false.
To verify if the substituted value satisfies the mathematical condition.

Key Concept

Solving One-Variable Inequalities
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Topics

Solving One-Variable Inequalities

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