Question

14 find the absolute value of a rational number ns0.1.1 interpret the absolute value of a rational number as the distance from zero on a number line \\( \boldsymbol{x} \\) given a real - world context (l4)
the temperature in alaska was \\( - 18.5^{\circ}\text{c} \\) during a winter storm.
how far below freezing is the temperature?
marias bank account shows a balance of \\( \\$ - 42.75 \\) after paying her bills.
how much will maria need to deposit so that her account has no debt?
15
15 ns0.1.4 solve mathematical problems with one operation involving absolute value
\\( \triangleright \\) or compare the absolute value of two numbers (l2)
use inequality symbols (\\( >, <, = \\)) to compare the values.
\\( |4.6| \bigcirc | - 4.6| \\)
\\( | - 3.2| \bigcirc | - 5.82| \\)
\\( | - 7.38| \bigcirc |2.13| \\)
use inequality symbols (\\( >, <, = \\)) to compare the values.
\\( |6.7| \bigcirc | - 7.6| \\)
\\( |9.35| \bigcirc | - 9.35| \\)
\\( | - 1.23| \bigcirc | - 1.1| \\)

Explanation:

Step1: Recall absolute value definition

The absolute value of a number \( x \), denoted \( |x| \), is the distance of \( x \) from 0 on the number line. For any real number \( x \), \( |x| = x \) if \( x \geq 0 \), and \( |x| = -x \) if \( x < 0 \).

Step2: Solve \( |4.6| \circ |-4.6| \)

• Calculate \( |4.6| \): Since \( 4.6 \geq 0 \), \( |4.6| = 4.6 \).
• Calculate \( |-4.6| \): Since \( -4.6 < 0 \), \( |-4.6| = -(-4.6) = 4.6 \).
• Compare: \( 4.6 = 4.6 \), so \( |4.6| = |-4.6| \).

Step3: Solve \( |-3.2| \circ |-5.82| \)

• Calculate \( |-3.2| \): \( |-3.2| = 3.2 \).
• Calculate \( |-5.82| \): \( |-5.82| = 5.82 \).
• Compare: \( 3.2 < 5.82 \), so \( |-3.2| < |-5.82| \).

Step4: Solve \( |-7.38| \circ |2.13| \)

• Calculate \( |-7.38| \): \( |-7.38| = 7.38 \).
• Calculate \( |2.13| \): \( |2.13| = 2.13 \).
• Compare: \( 7.38 > 2.13 \), so \( |-7.38| > |2.13| \).

Step5: Solve \( |6.7| \circ |-7.6| \)

• Calculate \( |6.7| \): \( |6.7| = 6.7 \).
• Calculate \( |-7.6| \): \( |-7.6| = 7.6 \).
• Compare: \( 6.7 < 7.6 \), so \( |6.7| < |-7.6| \).

Step6: Solve \( |9.35| \circ |-9.35| \)

• Calculate \( |9.35| \): \( |9.35| = 9.35 \).
• Calculate \( |-9.35| \): \( |-9.35| = 9.35 \).
• Compare: \( 9.35 = 9.35 \), so \( |9.35| = |-9.35| \).

Step7: Solve \( |-1.23| \circ |-1.1| \)

• Calculate \( |-1.23| \): \( |-1.23| = 1.23 \).
• Calculate \( |-1.1| \): \( |-1.1| = 1.1 \).
• Compare: \( 1.23 > 1.1 \), so \( |-1.23| > |-1.1| \).

Answer:

\( |4.6| \boldsymbol{=} |-4.6| \)
\( |-3.2| \boldsymbol{<} |-5.82| \)
\( |-7.38| \boldsymbol{>} |2.13| \)
\( |6.7| \boldsymbol{<} |-7.6| \)
\( |9.35| \boldsymbol{=} |-9.35| \)
\( |-1.23| \boldsymbol{>} |-1.1| \)