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Solve linear equations with variables on both sides

Twin Rivers has a population of 90,80090,800, and its population has been increasing by 800800 people each year. White Stone has a population of 87,20087,200, and its population has been increasing by 1,2001,200 people each year. These trends in population change are expected to continue.\newlineWhich equation can you use to find tt, the number of years it will take for the two cities to have the same population?\newlineChoices:\newline(A) 90,800+800t=87,200+1,200t90,800 + 800t = 87,200 + 1,200t\newline(B) 90,800−800t=87,200+1,200t90,800 - 800t = 87,200 + 1,200t\newlineHow long will it take for the two cities to have the same population?\newlineSimplify any fractions.\newline____ years\newline
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Caden and his little sister, Nina, went blackberry picking. Caden helped Nina get started until she had 4242 berries. When Caden started picking his own berries, he picked 1111 berries per minute while Nina continued to pick 55 berries per minute.\newlineWhich equation can you use to find mm, the number of minutes it took for Caden to have as many berries as Nina?\newlineChoices:\newline(A) 42+5m=11m42 + 5m = 11m\newline(B) 5m+11=42m5m + 11 = 42m\newlineAfter how many minutes did Caden have as many berries as Nina?\newlineSimplify any fractions.\newline____ minutes\newline
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Rashida was asked to determine whether f(x)=x2−∣x∣ f(x)=x^{2}-|x| is even, odd, or neither. Here is her work:\newlineStep 11: Find expression for f(−x) f(-x) \newlinef(−x)=(−x)2−∣(−x)∣=x2+∣x∣ \begin{aligned} f(-x) & =(-x)^{2}-|(-x)| \\ & =x^{2}+|x| \end{aligned} \newlineStep 22: Check if f(−x) f(-x) is equal to f(x) f(x) or −f(x) -f(x) \newlinex2+∣x∣ x^{2}+|x| isn't the same as f(x)=x2−∣x∣ f(x)=x^{2}-|x| or −f(x)=−x2+∣x∣ -f(x)=-x^{2}+|x| .\newlineStep 33: Conclusion\newlinef(−x) f(-x) isn't equivalent to either f(x) f(x) or −f(x) -f(x) , so f f is neither even nor odd.\newlineIs Rashida's work correct? If not, what is the first step where Rashida made a mistake?\newlineChoose 11 answer:\newline(A) Rashida's work is correct.\newline(B) Rashida's work is incorrect. She first made a mistake in Step 11.\newline(C) Rashida's work is incorrect. She first made a mistake in Step 22.\newline(D) Rashida's work is incorrect. She first made a mistake in Step 33.
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Felix was asked whether the following equation is an identity:\newline(x2+1)2=(x2−1)2+(2x)2 \left(x^{2}+1\right)^{2}=\left(x^{2}-1\right)^{2}+(2 x)^{2} \newlineHe performed the following steps:\newline(x2+1)2 \left(x^{2}+1\right)^{2} \newline↪ Step 1=x4+x2+x2+1 \stackrel{\text { Step } 1}{\hookrightarrow}=x^{4}+x^{2}+x^{2}+1 \newline↪ Step 2=x4+2x2+1 \stackrel{\text { Step } 2}{\hookrightarrow}=x^{4}+2 x^{2}+1 \newline↪ Step 3=x4+2x2+1−2x2+2x2 \stackrel{\text { Step } 3}{\hookrightarrow}=x^{4}+2 x^{2}+1-2 x^{2}+2 x^{2} \newline↪ Step 4=(x4−2x2+1)+4x2 \stackrel{\text { Step } 4}{\hookrightarrow}=\left(x^{4}-2 x^{2}+1\right)+4 x^{2} \newline↪ Step 5=(x2−1)2+(2x)2 \stackrel{\text { Step } 5}{\hookrightarrow}=\left(x^{2}-1\right)^{2}+(2 x)^{2} \newlineFor this reason, Felix stated that the equation is a true identity.\newlineIs Felix correct? If not, in which step did he make a mistake?\newlineChoose 11 answer:\newline(A) Felix is correct.\newline(B) Felix is incorrect. He made a mistake in step 11.\newline(C) Felix is incorrect. He made a mistake in step 33.\newline(D) Felix is incorrect. He made a mistake in step 55.
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Philip is downloading applications (apps) and songs to his tablet. He downloads 77 apps and 66 songs. Each song takes an average of 00.88 minutes longer to download than each app. If it takes 2121.77 minutes for his downloads to finish, which of the following systems could be used to approximate a a , the average number of minutes it takes to download one app, and s s , the average number of minutes it takes to download one song?\newlineChoose 11 answer:\newline(A) a+s=21.7 a+s=21.7 \newline6s=7a−0.8 6 s=7 a-0.8 \newline(B) a+s=21.7 a+s=21.7 \newline7a=6s−0.8 7 a=6 s-0.8 \newline(C) 7a+6s=21.7 7 a+6 s=21.7 \newlines=a−0.8 s=a-0.8 \newline(D) 7a+6s=21.7 7 a+6 s=21.7 \newlinea=s−0.8 a=s-0.8
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Liam deposits l l dollars into an account that earns 0.9% 0.9 \% in simple interest each year. Grace deposits g g dollars into an account that earns 1.1% 1.1 \% in simple interest each year. Both Liam and Grace let their money earn interest for one year and make no further deposits. If Liam's initial deposit was $800 \$ 800 more than Grace's, and if both Liam and Grace earn the same amount of interest after one year, which of the following systems of equations could be used to find their initial deposits?\newlineChoose 11 answer:\newline(A) 0.009l+800=0.011g 0.009 l+800=0.011 g \newlinel=g l=g \newline(B) 0.009l=0.011g+800 0.009 l=0.011 g+800 \newlinel=g l=g \newline(c) 0.009l=0.011g 0.009 l=0.011 g \newlinel+800=g l+800=g \newline(D) 0.009l=0.011g 0.009 l=0.011 g \newlinel=g+800 l=g+800
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