Question

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Answer 1

\(a,\left|x\right|+\dfrac{1}{2}=3\\ \Rightarrow\left|x\right|=3-\dfrac{1}{2}\\ \Rightarrow\left|x\right|=\dfrac{5}{2}\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{5}{2}\end{matrix}\right.\)

\(b,10,23-\left|x\right|=5\\ \Rightarrow\left|x\right|=10,23-5\\ \Rightarrow\left|x\right|=5,23\\ \Rightarrow\left[{}\begin{matrix}x=5,23\\x=-5,23\end{matrix}\right.\)

\(c,2\left|x\right|-\dfrac{1}{4}=\dfrac{2}{3}\\ \Rightarrow2\left|x\right|=\dfrac{2}{3}+\dfrac{1}{4}\\ \Rightarrow2\left|x\right|=\dfrac{11}{12}\\ \Rightarrow\left|x\right|=\dfrac{11}{12}:2\\ \Rightarrow\left|x\right|=\dfrac{11}{24}\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{24}\\x=-\dfrac{11}{24}\end{matrix}\right.\)

\(d,6-3\left|x\right|=\dfrac{3}{4}\\ \Rightarrow3\left|x\right|=6-\dfrac{3}{4}\\ \Rightarrow3\left|x\right|=\dfrac{21}{4}\\ \Rightarrow\left|x\right|=\dfrac{21}{4}:3\\ \Rightarrow\left|x\right|=\dfrac{7}{4}\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{4}\\x=-\dfrac{7}{4}\end{matrix}\right.\)

Answer 2

\(a)\left|x\right|+\dfrac{1}{2}=3\\ \left|x\right|=3-\dfrac{1}{2}\\ \left|x\right|=\dfrac{5}{2}\\ x=\left\{{}\begin{matrix}\dfrac{5}{2}\\-\dfrac{5}{2}\end{matrix}\right.\\ b)10,23-\left|x\right|=5\\ \left|x\right|=10,23-5\\ \left|x\right|=5,23\\ x=\left\{{}\begin{matrix}5,23\\-5,23\end{matrix}\right.\\ c)2\left|x\right|-\dfrac{1}{4}=\dfrac{2}{3}\\ 2\left|x\right|=\dfrac{2}{3}.\dfrac{1}{4}\\ 2\left|x\right|=\dfrac{11}{12}\\ \left|x\right|=\dfrac{11}{12}:2\\ \left|x\right|=\dfrac{11}{24}\\ x=\left\{{}\begin{matrix}\dfrac{11}{24}\\-\dfrac{11}{24}\end{matrix}\right.\)

\(d)6-3\left|x\right|=\dfrac{3}{4}\\ 3\left|x\right|=6-\dfrac{3}{4}\\ 3\left|x\right|=\dfrac{21}{4}\\ \left|x\right|=\dfrac{7}{4}\\ x=\left\{{}\begin{matrix}\dfrac{7}{4}\\-\dfrac{7}{4}\end{matrix}\right.\)