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Sagot :
To solve the absolute value inequality [tex]\( \frac{2|x-5|}{7} \geq 10 \)[/tex]:
First, isolate the absolute value expression:
[tex]\[ \frac{2|x-5|}{7} \geq 10 \][/tex]
Multiply both sides of the inequality by 7 to clear the denominator:
[tex]\[ 2|x-5| \geq 70 \][/tex]
Next, divide both sides by 2 to further isolate the absolute value:
[tex]\[ |x-5| \geq 35 \][/tex]
The absolute value inequality [tex]\( |x-5| \geq 35 \)[/tex] can be interpreted as two separate inequalities:
[tex]\[ x - 5 \geq 35 \quad \text{or} \quad x - 5 \leq -35 \][/tex]
Solve each inequality separately:
1. [tex]\( x - 5 \geq 35 \)[/tex]:
Add 5 to both sides:
[tex]\[ x \geq 40 \][/tex]
2. [tex]\( x - 5 \leq -35 \)[/tex]:
Add 5 to both sides:
[tex]\[ x \leq -30 \][/tex]
Thus, the solution to the inequality [tex]\( \frac{2|x-5|}{7} \geq 10 \)[/tex] consists of two parts:
[tex]\[ x \geq 40 \quad \text{or} \quad x \leq -30 \][/tex]
To summarize, the positive absolute value for [tex]\( x \)[/tex] is:
[tex]\[ \begin{array}{l} x \geq 40 \\ x \leq -30 \end{array} \][/tex]
First, isolate the absolute value expression:
[tex]\[ \frac{2|x-5|}{7} \geq 10 \][/tex]
Multiply both sides of the inequality by 7 to clear the denominator:
[tex]\[ 2|x-5| \geq 70 \][/tex]
Next, divide both sides by 2 to further isolate the absolute value:
[tex]\[ |x-5| \geq 35 \][/tex]
The absolute value inequality [tex]\( |x-5| \geq 35 \)[/tex] can be interpreted as two separate inequalities:
[tex]\[ x - 5 \geq 35 \quad \text{or} \quad x - 5 \leq -35 \][/tex]
Solve each inequality separately:
1. [tex]\( x - 5 \geq 35 \)[/tex]:
Add 5 to both sides:
[tex]\[ x \geq 40 \][/tex]
2. [tex]\( x - 5 \leq -35 \)[/tex]:
Add 5 to both sides:
[tex]\[ x \leq -30 \][/tex]
Thus, the solution to the inequality [tex]\( \frac{2|x-5|}{7} \geq 10 \)[/tex] consists of two parts:
[tex]\[ x \geq 40 \quad \text{or} \quad x \leq -30 \][/tex]
To summarize, the positive absolute value for [tex]\( x \)[/tex] is:
[tex]\[ \begin{array}{l} x \geq 40 \\ x \leq -30 \end{array} \][/tex]
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