Find the value of a, if:Modulus(2a-3)=3a+2
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\textbf{Concept:}Concept:
\text{If } |x|=u, \text{ then} \;x=\pm\;uIf ∣x∣=u, thenx=±u
\textbf{Given:}Given:
|2a-3|=3a+2∣2a−3∣=3a+2
\text{Using the given concept,}Using the given concept,
2a-3=\pm(3a+2)2a−3=±(3a+2)
\text{case(i):}case(i):
2a-3=3a+22a−3=3a+2
-2-3=3a-2a−2−3=3a−2a
\implies\bf\;a=-5⟹a=−5
\text{case(ii):}case(ii):
2a-3=-(3a+2)2a−3=−(3a+2)
2a-3=-3a-22a−3=−3a−2
2a+3a=3-22a+3a=3−2
5a=15a=1
\implies\bf\;a=\frac{1}{5}⟹a=51
\text{But a=-5 does not satisfy the given equation }But a=-5 does not satisfy the given equation
\therefore\text{The solution is }\bf\;a=\frac{1}{5}∴The solution is a=51
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