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Raul tried to evaluate an expression step by step.

{:[3-(-5)-7],[=3+5-7quad" Step "1],[=3+2quad" Step 2 "],[=5quad" Step "3]:}
Find Raul's first mistake.
Choose 1 answer:
(A) The opposite of -5 is -5 , not 5.
(B) 5 minus 7 equals -2 , not 2.
(c) 3 plus 2 equals 6 , not 5 .

Raul tried to evaluate an expression step by step. $\newline$ $\begin{array}{l} 3-(-5)-7 \\ =3+5-7 \quad \text { Step } 1 \\ =3+2 \quad \text { Step 2 } \\ =5 \quad \text { Step } 3 \\ \end{array}$ $\newline$ Find Raul's first mistake. $\newline$ Choose $1$ answer: $\newline$ (A) The opposite of $-5$ is $-5$ , not $5$ . $\newline$ (B) $5$ minus $7$ equals $-2$ , not $2$ . $\newline$ (C) $3$ plus $2$ equals $6$ , not $5$ .

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Solve a system of equations using any method: word problems

Full solution

Q. Raul tried to evaluate an expression step by step.

\newline

\begin{array}{l} 3-(-5)-7 \\ =3+5-7 \quad \text { Step } 1 \\ =3+2 \quad \text { Step 2 } \\ =5 \quad \text { Step } 3 \\ \end{array}

\newline

Find Raul's first mistake.

\newline

Choose

1

answer:

\newline

(A) The opposite of

-5

is

-5

, not

5

.

\newline

(B)

5

minus

7

equals

-2

, not

2

.

\newline

(C)

3

plus

2

equals

6

, not

5

.

Initial Expression: Raul's initial expression is $3 - (-5) - 7$ . He starts by converting the subtraction of a negative number to addition: $3 - (-5)$ becomes $3 + 5$ . This is a correct application of the rule that subtracting a negative is the same as adding a positive. Calculation: $3 + 5 = 8$ .
Conversion to Addition: Next, Raul subtracts $7$ from the result of the first step: $8 - 7$ . Calculation: $8 - 7 = 1$ . Raul incorrectly states the result as $3 + 2$ in ＂Step $2$ ＂. This is where the first mistake occurs.

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\newline

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\newline

The relationship between the elapsed time

t

, in hours, since Dominic sent the letter, and the number of people,

P_{\text {hour }}(t)

, who receive the email is modeled by the following function:

\newline

P_{\text {hour }}(t)=18 \cdot(1.05)^{t}

\newline

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Every day, the number of people who receive the email grows by a factor of

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Question

Jessie tried to solve an equation step by step.

\newline

1.5 b+9=11

\newline

1.5 b=3 \quad \text { Step } 1

\newline

b=2 \quad \text { Step } 2

\newline

Find Jessie's mistake.

\newline

1

\newline

1

\newline

2

\newline

(C) Jessie did not make a mistake.

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Question

Leon tried to solve an equation step by step.

\newline

\begin{aligned} \frac{1}{2} w-12 & =18 \\ \frac{1}{2} w & =30 \quad \text { Step } 1 \\ w & =15 \quad \text { Step 2 } \end{aligned}

\newline

Find Leon's mistake.

\newline

1

\newline

\operatorname{Step} 1

\newline

2

\newline

(C) Leon did not make a mistake.

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Question

Olga tried to solve an equation step by step.

\newline

\begin{array}{rlrl} \frac{1}{4}\left(\frac{1}{3} k+9\right) & =6 & \\ \frac{1}{3} k+9 & =24 \quad \text { Step 1 } \\ \frac{1}{3} k & =15 \quad \text { Step 2 } \\ k & =5 \quad \text { Step 3 } \end{array}

\newline

Find Olga's mistake.

\newline

1

\newline

1

\newline

2

\newline

\operatorname{Step} 3

\newline

D Olga did not make a mistake.

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Question

7

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\$ 8.96

\newline

Which equation would help determine the cost of

5

\newline

1

\newline

\frac{x}{5}=\frac{\$ 8.96}{7}

\newline

\frac{x}{5}=\frac{7}{\$ 8.96}

\newline

\frac{7}{5}=\frac{x}{\$ 8.96}

\newline

\frac{5}{x}=\frac{\$ 8.96}{7}

\newline

(E) None of the above

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Question

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\newline

1

\newline

\sqrt{2}

\newline

2

\newline

4

\newline

(D) The limit doesn't exist

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