Solve for $$ x $$. $$ \frac{1}{2}\left(\frac{3}{5} x-\frac{1}{2}\right)x+\frac{3}{8} $$ $$ x\frac{25}{28} $$ $$ x

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Solve for $$ x $$. $$ \frac{1}{2}\left(\frac{3}{5} x-\frac{1}{2}\right)>x+\frac{3}{8} $$ $$ x>\frac{25}{28} $$ $$ x<-\frac{25}{28} $$ $$ x<\frac{25}{28} $$ $$ x>-\frac{25}{28} $$

UpStudy AI · Accepted Answer

To solve the inequality: $$ \frac{1}{2}\left(\frac{3}{5} x - \frac{1}{2}\right) > x + \frac{3}{8} $$ **Step 1: Eliminate the Fraction** Multiply both sides of the inequality by 2 to eliminate the $$\frac{1}{2}$$: $$ \frac{3}{5}x - \frac{1}{2} > 2x + \frac{3}{4} $$ **Step 2: Combine Like Terms** Bring all $$x$$-terms to one side and constant terms to the other side: $$ \frac{3}{5}x - 2x > \frac{3}{4} + \frac{1}{2} $$ Simplify the left side: $$ \frac{3}{5}x - \frac{10}{5}x = -\frac{7}{5}x $$ Simplify the right side: $$ \frac{3}{4} + \frac{1}{2} = \frac{5}{4} $$ So the inequality becomes: $$ -\frac{7}{5}x > \frac{5}{4} $$ **Step 3: Solve for $$x$$** Divide both sides by $$-\frac{7}{5}$$. Remember, dividing by a negative number reverses the inequality sign: $$ x < \frac{5}{4} \div \left(-\frac{7}{5}\right) = -\frac{25}{28} $$ **Conclusion** The solution to the inequality is: $$ x < -\frac{25}{28} $$ **Answer:** $$ x < -\dfrac{25}{28} $$ $$ x < -\frac{25}{28} $$

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