Linear expressions with fractional coefficients

Fractional coefficients still count equal units

For 2x/3-(3(x-5))/2, use sixths: [4x-9(x-5)]/6 = (45-5x)/6. The subtraction applies to the entire second numerator. Test a value such as x = 3 in both forms to detect a lost bracket.

Keep the whole subtracted numerator

For x/2-(x + 1)/3, use sixths to obtain [3x-2(x + 1)]/6 = (x-2)/6. The negative sign multiplies both terms inside the second bracket. At x = 2, both original and simplified forms equal zero.

Check your understanding 1 Use a common denominator

Simplify 3x/4-(x-2)/2.

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Write both in quarters: [3x-2(x-2)]/4 = (x + 4)/4. Subtracting only x and leaving the −2 unchanged would lose the bracket’s sign.