Solve the absolute value inequality 3|7x|+8≤6 .(1 point)

Question

Responses

[−221,221]
left bracket negative Start Fraction 2 over 21 End Fraction comma Start Fraction 2 over 21 End Fraction right bracket

(−∞,−221]∪[221,∞)
left parenthesis negative infinity comma negative Start Fraction 2 over 21 End Fraction right bracket union left bracket Start Fraction 2 over 21 End Fraction comma infinity right parenthesis

(−∞,∞)
left parenthesis negative infinity comma infinity right parenthesis

no solution

Answer 1

To solve the absolute value inequality \(3|7x| + 8 \leq 6\), we start by isolating the absolute value term.

1. Subtract 8 from both sides: \[ 3|7x| \leq 6 - 8 \] \[ 3|7x| \leq -2 \]

2. Divide both sides by 3: \[ |7x| \leq -\frac{2}{3} \]

Since the absolute value of any expression cannot be negative, \( |7x| \leq -\frac{2}{3} \) implies that there are no values of \( x \) that satisfy this inequality.

Therefore, the solution to the inequality is:

no solution.