Solve for z.−∣z∣>−3Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.______
Q. Solve for z.−∣z∣>−3Write 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 term: We have the inequality:−∣z∣>−3First, we need to isolate the absolute value term. To do this, we can multiply both sides of the inequality by −1, remembering that this reverses the inequality sign.−1⋅(−∣z∣)<−1⋅(−3)
Multiply by −1: After multiplying by −1, we get:∣z∣<3This means that z must be less than 3 and greater than −3, because the absolute value of z is less than 3.
Write compound inequality: Now we can write the compound inequality that represents the solution to the inequality ∣z∣<3:−3<z<3This is the compound inequality that describes all the values of z that satisfy the original inequality.
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