Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #81 : Solving Equations

A tank can fill a swimming pool in two hours. A hose can fill the same swimming pool in three hours. How long will it take in hours if both the tank and hose fill the swimming pool at the same time?

Possible Answers:

\displaystyle 2\frac{1}{2}

\displaystyle 1

\displaystyle 1\frac{1}{2}

\displaystyle 1\frac{1}{6}

\displaystyle 1\frac{1}{5}

Correct answer:

\displaystyle 1\frac{1}{5}

Explanation:

Let's set-up an equation.

\displaystyle \frac{x}{2}+\frac{x}{3}=1

\displaystyle x represents the time they will take together and \displaystyle 1 represents the job both the tank and hose finish as a whole

Find the common denominator and add the fractions. \displaystyle \frac{5x}{6}=1. Cross-multiply.

\displaystyle 5x=6 Divide \displaystyle 5 on both sides.

\displaystyle x=\frac{6}{5}or 1 \frac{1}{5} hours

Example Question #91 : Solving Equations

Solve for \displaystyle x.

\displaystyle x+902=-345

Possible Answers:

\displaystyle -1523

\displaystyle -557

\displaystyle 557

\displaystyle -1347

\displaystyle -1247

Correct answer:

\displaystyle -1247

Explanation:

\displaystyle x+902=-345 Subtract \displaystyle 902 on both sides. When adding two negative numbers, we just add the numbers and put a minus sign in the end.

\displaystyle x=-1247

Example Question #92 : Solving Equations

Solve for \displaystyle x.

\displaystyle x+578=239

Possible Answers:

\displaystyle 923

\displaystyle 817

\displaystyle -817

\displaystyle -339

\displaystyle 339

Correct answer:

\displaystyle -339

Explanation:

\displaystyle x+578=239 Subtract \displaystyle 578 on both sides. Since \displaystyle 578 is greater than \displaystyle 239 and is negative, our answer is negative. We treat as a normal subtraction problem.

\displaystyle x=-339

Example Question #92 : Solving Equations

Solve for \displaystyle x.

\displaystyle 7x+29=176

Possible Answers:

\displaystyle 19

\displaystyle 29

\displaystyle 31

\displaystyle 21

\displaystyle 39

Correct answer:

\displaystyle 21

Explanation:

\displaystyle 7x+29=176 Subtract \displaystyle 29 on both sides.

\displaystyle 7x=147 Divide \displaystyle 7 on both sides.

\displaystyle x=21

Example Question #2411 : Algebra Ii

Solve for \displaystyle x.

\displaystyle x-138=934

Possible Answers:

\displaystyle 1082

\displaystyle 796

\displaystyle 848

\displaystyle 824

\displaystyle 1072

Correct answer:

\displaystyle 1072

Explanation:

\displaystyle x-138=934 Add \displaystyle 138 on both sides.

\displaystyle x=1072

Example Question #222 : Equations

Solve for \displaystyle x.

\displaystyle x-345=-378

Possible Answers:

\displaystyle -23

\displaystyle 33

\displaystyle 723

\displaystyle -33

\displaystyle -723

Correct answer:

\displaystyle -33

Explanation:

\displaystyle x-345=-378 Add \displaystyle 345 on both sides. Since \displaystyle 378 is greater than \displaystyle 345 and is negative, our answer is negative. We treat as a subtraction problem.

\displaystyle x=-33

Example Question #223 : Equations

Solve for \displaystyle x.

\displaystyle 5x-129=236

Possible Answers:

\displaystyle 63

\displaystyle 73

\displaystyle 68

\displaystyle 78

\displaystyle 83

Correct answer:

\displaystyle 73

Explanation:

\displaystyle 5x-129=236 Add \displaystyle 129 on both sides.

\displaystyle 5x=365 Divide \displaystyle 5 on both sides.

\displaystyle x=73

Example Question #2412 : Algebra Ii

Solve for \displaystyle x.

\displaystyle x-13=2x+25

Possible Answers:

\displaystyle 38

\displaystyle -38

\displaystyle -12

\displaystyle 26

\displaystyle 12

Correct answer:

\displaystyle -38

Explanation:

\displaystyle x-13=2x+25 Add \displaystyle 13 on both sides.

\displaystyle x=2x+38 Subtract \displaystyle 2x on both sides. 

\displaystyle -x=38 Divide both sides by \displaystyle -1.

\displaystyle x=-38

Example Question #94 : Solving Equations

Solve for \displaystyle x.

\displaystyle x+19=4x-56

Possible Answers:

\displaystyle 25

\displaystyle 20

\displaystyle -25

\displaystyle 15

\displaystyle 15

Correct answer:

\displaystyle 25

Explanation:

\displaystyle x+19=4x-56 Add \displaystyle 56 on both sides.

\displaystyle x+75=4x Subtract \displaystyle x on both sides.

\displaystyle 75=3x Divide \displaystyle 3 on both sides.

\displaystyle 25=x

Example Question #92 : Solving Equations

Solve for \displaystyle x.

\displaystyle 4(x-12)=96

Possible Answers:

\displaystyle 24

\displaystyle 34

\displaystyle 28

\displaystyle 48

\displaystyle 36

Correct answer:

\displaystyle 36

Explanation:

There are TWO ways:

Method \displaystyle 1:

\displaystyle 4(x-12)=96 Distribute the \displaystyle 4.

\displaystyle 4x-48=96 Add \displaystyle 48 on both sides.

\displaystyle 4x=144 Divide \displaystyle 4 on both sides.

\displaystyle x=36

 

Method \displaystyle 2:

\displaystyle 4(x-12)=96 Divide \displaystyle 4 on both sides.

\displaystyle x-12=24 Add \displaystyle 12 on both sides.

\displaystyle x=36

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