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Graphing the Inequality

What are the two equations created by the inequality [tex]|x-12|+5\ \textless \ 27[/tex]?

[tex]y_1 = \square[/tex]

[tex]y_2 = \square[/tex]


Sagot :

Sure! Let's solve the inequality step by step.

1. Start with the given inequality:
[tex]\[ |x - 12| + 5 < 27 \][/tex]

2. Subtract 5 from both sides to isolate the absolute value term:
[tex]\[ |x - 12| < 22 \][/tex]

3. To remove the absolute value, we need to create two separate inequalities:
[tex]\[ x - 12 < 22 \][/tex]
and
[tex]\[ -(x - 12) < 22 \][/tex]

4. Solve the first inequality:
[tex]\[ x - 12 < 22 \implies x < 34 \][/tex]

5. Solve the second inequality. Start by distributing the negative sign:
[tex]\[ -(x - 12) < 22 \implies x - 12 > -22 \][/tex]
Then add 12 to both sides:
[tex]\[ x > -10 \][/tex]

So, the two equations created by the inequality are:
[tex]\[ y_1 = x < 34 \][/tex]
[tex]\[ y_2 = x > -10 \][/tex]

Hence, the inequalities are:
[tex]\[ x < 34 \quad \text{and} \quad x > -10 \][/tex]