1.1E: Exercises - Solving Linear Equations in One Variable

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Jun 27, 2024
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- 1.1: Solving Linear Equations in One Variable
- 1.2: Solving Linear Equations in Two Variables

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Exercise $\PageIndex{1}$

Determine whether or not the given value is a solution.

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

Answer

1. No

3. Yes

5. No

Exercise $\PageIndex{2}$

Solve.

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

Answer

1. $6$

3. $0$

5. $−\frac{5}{4}$

7. $−15$

9. $\frac{3}{4}$

11. $−3$

Exercise $\PageIndex{3}$

Solve.

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

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

When $3$ is subtracted from the sum of a number and $10$ the result is $2$ . Find the number.
The sum of $3$ times a number and $12$ is equal to $3$ . Find the number.
Three times the sum of a number and $6$ is equal to $5$ times the number. Find the number.
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.”

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Exercise 1.1E.1\PageIndex{1}

Exercise 1.1E.2\PageIndex{2}

Exercise 1.1E.3\PageIndex{3}

Exercise 1.1E.4\PageIndex{4}

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Exercise $\PageIndex{1}$

Exercise $\PageIndex{2}$

Exercise $\PageIndex{3}$

Exercise $\PageIndex{4}$