Equivalent Linear Expressions - Instruction - Level (4) Write an expression that is equivalent to \( \frac{1}{4} x+1+\frac{3}{4} x-\frac{2}{3}-\frac{1}{2} x \). (4) First write the expression \( \frac{1}{4} x+1+\frac{3}{4} x-\frac{2}{3}-\frac{1}{2} x \) as a sum. \( \frac{1}{4} x+1+\frac{3}{4} x-\frac{2}{3}-\frac{1}{2} x=\frac{1}{4} x+1+\frac{3}{4} x+(\square)+(\square x \) (4) Subtracting is the same as adding the opposite.

To simplify the given expression, start by converting the subtractions into additions of the opposites. Therefore, rewrite the expression as: \(\frac{1}{4} x + 1 + \frac{3}{4} x + \left(-\frac{2}{3}\right) + \left(-\frac{1}{2} x\right)\). This transforms your expression into a sum, making it easier to combine like terms. Next, combine the coefficients of \(x\) and the constant terms separately. \( \frac{1}{4} x + \frac{3}{4} x - \frac{1}{2} x \) translates to \( x - \frac{1}{2} x = \frac{1}{4} x \). For the constants, \( 1 - \frac{2}{3} \) simplifies to \(\frac{1}{3}\). Thus, the equivalent expression is \( \frac{1}{4} x + \frac{1}{3} \).