Q. Solve for all values of b in simplest form.10=∣7−2b∣Answer: b=
Understand absolute value equation: Understand the absolute value equation.The absolute value equation is 10=∣7−2b∣. We need to solve for b.
Set up two equations: Set up two separate equations to account for the absolute value.Since the absolute value of a number can be either positive or negative, we have two cases:Case 1: 7−2b=10Case 2: 7−2b=−10
Solve for b in Case 1: Solve for b in Case 1.Starting with 7−2b=10, we subtract 7 from both sides to isolate the term with b.7−2b−7=10−7−2b=3Now, divide both sides by −2 to solve for b.b=3/(−2)b=−3/2
Solve for b in Case 2: Solve for b in Case 2.Starting with 7−2b=−10, we subtract 7 from both sides to isolate the term with b.7−2b−7=−10−7−2b=−17Now, divide both sides by −2 to solve for b.b=−17/(−2)b=17/2
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