The other solution of the given equation is: x = - 4.
What is an equation?
"An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign."
Given, [tex]3 - 2|0.5x + 1.5| = 2[/tex]
⇒ [tex]2|0.5x + 1.5| = 3 - 2[/tex]
⇒ [tex]2|0.5x + 1.5| = 1[/tex]
⇒ [tex]|0.5x + 1.5| = 1/2[/tex]
⇒ [tex](0.5x + 1.5)^{2} = (\frac{1}{2})^{2}[/tex]
⇒ [tex](0.5x)^{2} + 2(0.5x)(1.5) + (1.5)^{2} = (0.5)^{2}[/tex]
⇒ [tex]0.25x^{2} + 1.5x + 2.25 = 0.25[/tex]
⇒ [tex]0.25x^{2} + 1.5x + 2.25 - 0.25 = 0[/tex]
⇒ [tex]0.25x^{2} + 1.5x + 2 = 0[/tex]
⇒ [tex]x = [- 1.5[/tex] ± [tex]{\sqrt{{(1.5)^{2} - 4 (0.25)(2)}}} ]/2(0.25)[/tex]
⇒ [tex]x = [- 1.5[/tex] ± [tex][{\sqrt{(2.25)^{2} - 2}}]/{0.5}[/tex]
⇒ [tex]x = [- 1.5[/tex] ± √(0.25 ]/0.5
⇒ x = [- 1.5 ± 0.5 ]/0.5
Therefore, x = (- 1.5 - 0.5)/0.5 = - 4
Again, x = (- 1.5 + 0.5)/0.5 = - 2
The other solution will be: x = - 4.
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