Q. Solve for v.∣v∣−7>−2Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.
Isolate absolute value: We have the inequality:∣v∣−7>−2First, we isolate the absolute value term by adding 7 to both sides of the inequality.∣v∣−7+7>−2+7∣v∣>5
Interpret absolute value: Now we interpret the absolute value inequality.The inequality ∣v∣>5 means that v is more than 5 units away from 0 on the number line. This leads to two separate inequalities:v>5 or v<−5
Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality.The compound inequality is:v>5 or v<−5
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