2.1E: Exercises - Solving Linear Inequalities in One Variable

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Exercise $\PageIndex{1}$

Determine whether or not the given value is a solution.

$5 x - 1 < - 2 ; x = - 1$
$- 3 x + 1 > - 10 ; x = 1$
$2 x - 3 < - 5 ; x = 1$
$5 x - 7 < 0 ; x = 2$
$9 y - 4 \geq 5 ; y = 1$
$- 6 y + 1 \leq 3 ; y = - 1$

Answer

1. Yes

3. No

5. Yes

Exercise $\PageIndex{2}$

Graph all solutions on a number line and provide the corresponding interval notation.

$3 x + 5 > - 4$
$2 x + 1 > - 1$
$6 - a \leq 6$
$- 2 a + 5 > 5$
$\frac { 5 x + 6 } { 3 } \leq 7$
$\frac { 4 x + 11 } { 6 } \leq \frac { 1 } { 2 }$
$2 ( 3 x + 14 ) < - 2$
$5 ( 2 y + 9 ) > - 15$
$5 x - 2 ( x - 3 ) < 3 ( 2 x - 1 )$
$3 ( 2 x - 1 ) - 10 > 4 ( 3 x - 2 ) - 5 x$

Answer

1. $( - 3 , \infty )$;

$a2d07ff66453c86a51eb9ee5ca94a731.png$ Figure 1.8.13

3. $[ 0 , \infty )$;

5. $( - \infty , 3 ]$;

7. $( - \infty , - 5 )$;

9. $( 3 , \infty )$;

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 \(\PageIndex{1}\)

Exercise \(\PageIndex{2}\)

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