# 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. $$5 (2t − 1) = 2 − t; t = 2$$

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. $$\frac{2 − 5y}{6} = −8$$

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. $$\frac{3}{2} a = \frac{3}{4} (1 + 2a) −\frac{1}{5} (a + 5)$$

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.

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.