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1.1E: Exercises - Solving Linear Equations in One Variable

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    Exercise \(\PageIndex{1}\)

    Determine whether or not the given value is a solution.

    1. \(−5x + 4 = −1 ; x = −1\)
    2. \(4x − 3 = −7 ; x = −1\)
    3. \(3y − 4 = 5; y = \frac{9}{3}\)
    4. \(−2y + 7 = 12 ; y = −\frac{5}{2}\)
    5. \(3a − 6 = 18 − a; a = −3\)
    6. \(5 (2t − 1) = 2 − t; t = 2\)
    Answer

    1. No

    3. Yes

    5. No

    Exercise \(\PageIndex{2}\)

    Solve.

    1. \(5x − 3 = 27\)
    2. \(6x − 7 = 47\)
    3. \(9a + 10 = 10\)
    4. \(5 − 3a = 5\)
    5. \(−8t + 5 = 15\)
    6. \(−9t + 12 = 33\)
    7. \(7 − y = 22\)
    8. \(6 − y = 12\)
    9. \(\frac{2}{3} x + \frac{1}{2} = 1\)
    10. \(\frac{3}{8} x + \frac{5}{4} = \frac{3}{2}\)
    11. \(\frac{1 − 3y}{5} = 2\)
    12. \(\frac{2 − 5y}{6} = −8\)
    Answer

    1. \(6\)

    3. \(0\)

    5. \(−\frac{5}{4}\)

    7. \(−15\)

    9. \(\frac{3}{4}\)

    11. \(−3\)

     

    Exercise \(\PageIndex{3}\)

    Solve.

    1. \(6x − 5 + 2x = 19\)
    2. \(7 − 2x + 9 = 24\)
    3. \(5y − 6 − 9y = 3 − 2y + 8\)
    4. \(7 − 9y + 12 = 3y + 11 − 11y\)
    5. \(\frac{1}{3} x −\frac{3}{2} + \frac{5}{2} x = \frac{5}{6} x + \frac{1}{4}\)
    6. \(\frac{5}{8} + \frac{1}{5} x −\frac{3}{4} = \frac{3}{10} x − \frac{1}{4}\)
    7. \(5 (y + 2) = 3 (2y − 1) + 10\)
    8. \(7 (y − 3) = 4 (2y + 1) − 21\)
    9. \(7 − 5 (3t − 9) = 22\)
    10. \(10 − 5 (3t + 7) = 20\)
    11. \(4 (4a − 1) = 5 (a − 3) + 2 (a − 2)\)
    12. \(6 (2b − 1) + 24b = 8 (3b − 1)\)
    13. \(\frac{2}{3} (x + 18) + 2 = \frac{1}{3} x − 13\)
    14. \(\frac{2}{5} x − \frac{1}{2} (6x − 3) = \frac{4}{3}\)
    15. \(\frac{1}{5} (2a + 3) −\frac{1}{2} = \frac{1}{3} a + \frac{1}{10}\)
    16. \(\frac{3}{2} a = \frac{3}{4} (1 + 2a) −\frac{1}{5} (a + 5)\)
    Answer

    1. \(3\)

    3. \(−\frac{17}{2}\)

    5. \(\frac{7}{8}\)

    7. \(3\)

    9. \(2\)

    11. \(−\frac{5}{3}\)

    13. \(−81\)

    15. \(0\)

    Exercise \(\PageIndex{4}\)

    Set up an algebraic equation then solve.

    Number Problems

    1. When \(3\) is subtracted from the sum of a number and \(10\) the result is \(2\). Find the number.
    2. The sum of \(3\) times a number and \(12\) is equal to \(3\). Find the number.
    3. Three times the sum of a number and \(6\) is equal to \(5\) times the number. Find the number.
    4. Twice the sum of a number and \(4\) is equal to \(3\) times the sum of the number and \(1\). Find the number.
    Answer

    1. \(−5\)

    3. \(9\)

     

    Footnotes

    138Linear expressions related with the symbols \(≤, <, ≥,\) and \(>\).

    139A real number that produces a true statement when its value is substituted for the variable.

    140Properties used to obtain equivalent inequalities and used as a means to solve them.

    141Inequalities that share the same solution set.

    142Two or more inequalities in one statement joined by the word “and” or by the word “or.”

    1.1E: Exercises - Solving Linear Equations in One Variable is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.