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Algebra II : Solving Equations

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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:

$2\frac{1}{2}$ $\displaystyle 2\frac{1}{2}$

$\displaystyle 1$

$1\frac{1}{2}$ $\displaystyle 1\frac{1}{2}$

$1\frac{1}{6}$ $\displaystyle 1\frac{1}{6}$

$1\frac{1}{5}$ $\displaystyle 1\frac{1}{5}$

Correct answer:

$1\frac{1}{5}$ $\displaystyle 1\frac{1}{5}$

Explanation:

Let's set-up an equation.

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

$\displaystyle x$ 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. $\frac{5x}{6}=1$ $\displaystyle \frac{5x}{6}=1$ . Cross-multiply.

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

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

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Example Question #91 : Solving Equations

Solve for $\displaystyle x$ .

$\displaystyle x+902=-345$

Possible Answers:

$\displaystyle -1523$

$\displaystyle -557$

557 $\displaystyle 557$

$\displaystyle -1347$

$\displaystyle -1247$

Correct answer:

$\displaystyle -1247$

Explanation:

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

x=-1247 $\displaystyle x=-1247$

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Example Question #92 : Solving Equations

Solve for $\displaystyle x$ .

$\displaystyle x+578=239$

Possible Answers:

923 $\displaystyle 923$

817 $\displaystyle 817$

$\displaystyle -817$

$\displaystyle -339$

339 $\displaystyle 339$

Correct answer:

$\displaystyle -339$

Explanation:

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

x=-339 $\displaystyle x=-339$

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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.

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

x=21 $\displaystyle x=21$

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Example Question #2411 : Algebra Ii

Solve for $\displaystyle x$ .

$\displaystyle x-138=934$

Possible Answers:

1082 $\displaystyle 1082$

796 $\displaystyle 796$

848 $\displaystyle 848$

824 $\displaystyle 824$

1072 $\displaystyle 1072$

Correct answer:

1072 $\displaystyle 1072$

Explanation:

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

x=1072 $\displaystyle x=1072$

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Example Question #222 : Equations

Solve for $\displaystyle x$ .

$\displaystyle x-345=-378$

Possible Answers:

$\displaystyle -23$

$\displaystyle 33$

723 $\displaystyle 723$

$\displaystyle -33$

$\displaystyle -723$

Correct answer:

$\displaystyle -33$

Explanation:

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

x=-33 $\displaystyle x=-33$

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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 129 $\displaystyle 129$ on both sides.

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

x=73 $\displaystyle x=73$

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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.

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

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

x=-38 $\displaystyle x=-38$

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Example Question #94 : Solving Equations

Solve for $\displaystyle x$ .

$\displaystyle x+19=4x-56$

Possible Answers:

$\displaystyle 25$

$\displaystyle 20$

$\displaystyle -25$

$\displaystyle 15$

Correct answer:

$\displaystyle 25$

Explanation:

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

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

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

25=x $\displaystyle 25=x$

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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.

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

x=36 $\displaystyle x=36$

Method $\displaystyle 2$ :

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

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

x=36 $\displaystyle x=36$

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Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #81 : Solving Equations

Example Question #91 : Solving Equations

Example Question #92 : Solving Equations

Example Question #92 : Solving Equations

Example Question #2411 : Algebra Ii

Example Question #222 : Equations

Example Question #223 : Equations

Example Question #2412 : Algebra Ii

Example Question #94 : Solving Equations

Example Question #92 : Solving Equations

All Algebra II Resources

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