Question:
Adler and Erika solved the same equation using the calculations below.
Adler’s Work
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
[tex]\frac{13}{8} - \frac{1}{2} = k + \frac{1}{2} -\frac{1}{2}[/tex]
[tex]\frac{9}{8}= k[/tex]
Erika’s Work
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
[tex]\frac{13}{8}+ (-\frac{1}{2}) = k + \frac{1}{2} + (-\frac{1}{2}).[/tex]
[tex]\frac{9}{8}= k[/tex]
Which statement is true about their work?
Answer:
Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.
Step-by-step explanation:
Given
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
Required
What is true about Adler and Erika's workings
Analyzing Adler's work;
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
Adler subtracted 1/2 from both sides
[tex]\frac{13}{8} - \frac{1}{2} = k + \frac{1}{2} -\frac{1}{2}[/tex]
Solving the expression on the left-hand side
[tex]\frac{13}{8} - \frac{1}{2} = \frac{13 - 4}{8} = \frac{9}{8}[/tex]
Solving the expression on the right-hand side
[tex]k + \frac{1}{2} - \frac{1}{2} = k[/tex]
Hence:
[tex]\frac{9}{8}= k[/tex]
So, Adler's workings is correct
Analyzing Erika's work;
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
Erika added -1/2 to both sides
[tex]\frac{13}{8}+ (-\frac{1}{2}) = k + \frac{1}{2} + (-\frac{1}{2}).[/tex]
Solving the expression on the left-hand side
[tex]\frac{13}{8} + (-\frac{1}{2}) = \frac{13}{8} - \frac{1}{2} = \frac{13 - 4}{8} = \frac{9}{8}[/tex]
Solving the expression on the right-hand side
[tex]k + \frac{1}{2} + (-\frac{1}{2}) =k + \frac{1}{2} - \frac{1}{2} = k[/tex]
Hence:
[tex]\frac{9}{8}= k[/tex]
So, Erika's workings is correct
Both workings are correct
Answer: Both Adler and Erika are correct
Step-by-step explanation:
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