Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #621 : Basic Single Variable Algebra

Solve for \displaystyle x.

\displaystyle -2x=1046

Possible Answers:

\displaystyle 662

\displaystyle -533

\displaystyle -523

\displaystyle 481

\displaystyle 543

Correct answer:

\displaystyle -523

Explanation:

To solve for the variable perform opposite operations to isolate it on one side of the equation with all constants on the other side.

\displaystyle -2x=1046 

Divide \displaystyle -2 on both sides.

\displaystyle x=-523

Example Question #271 : Equations

Solve for \displaystyle x.

\displaystyle -73x=-1314

Possible Answers:

\displaystyle 24

\displaystyle -26

\displaystyle 18

\displaystyle 14

\displaystyle -28

Correct answer:

\displaystyle 18

Explanation:

To solve for the variable perform opposite operations to isolate it on one side of the equation with all constants on the other side.

\displaystyle -73x=-1314 

Divide \displaystyle -73 on both sides.

\displaystyle x=18

Example Question #32 : Systems Of Equations

Solve for \displaystyle x:

\displaystyle 8(x+5)=16

Possible Answers:

\displaystyle 3

\displaystyle -\frac{11}{8}

None of the other answers

\displaystyle \frac{11}{8}

\displaystyle -3

Correct answer:

\displaystyle -3

Explanation:

First, you must multiply the left side of the equation using the distributive property.

This gives you \displaystyle 8x+40=16.

Next, subtract \displaystyle 40 from both sides to get \displaystyle 8x=-24.

Then, divide both sides by \displaystyle 8 to get \displaystyle x=-3.

Example Question #273 : Equations

Solve for \displaystyle x.

\displaystyle x+88.45=37.91

Possible Answers:

\displaystyle 68.44

\displaystyle -50.54

\displaystyle -46.92

\displaystyle 24.65

\displaystyle 32.66

Correct answer:

\displaystyle -50.54

Explanation:

In order to solve for \displaystyle x, we need to isolate the variable on the left side of the equation. We will do this by performing the same operations on both sides of the equation.

\displaystyle x+88.45=37.91 

Subtract \displaystyle 88.45 from both sides of the equation.

\displaystyle x+88.45-88.45=37.91-88.45

Solve.

\displaystyle x=-50.54

Example Question #271 : Equations

Solve for \displaystyle x.

\displaystyle x+445.78=-235.1

Possible Answers:

\displaystyle -680.88

\displaystyle -598.62

\displaystyle 726.66

\displaystyle 968.52

\displaystyle 482.10

Correct answer:

\displaystyle -680.88

Explanation:

In order to solve for \displaystyle x, we need to isolate the variable on the left side of the equation. We will do this by performing the same operations on both sides of the equation.

\displaystyle x+445.78=-235.1 

Subtract \displaystyle 445.78 from both sides of the equation.

\displaystyle x+445.78-445.78=-235.1-445.78

Solve.

\displaystyle x=-680.88

Example Question #145 : Solving Equations

Solve for \displaystyle x.

\displaystyle x-234.67=98.54

Possible Answers:

\displaystyle 333.21

\displaystyle 485.11

\displaystyle -149.56

\displaystyle -201.89

\displaystyle -136.13

Correct answer:

\displaystyle 333.21

Explanation:

In order to solve for \displaystyle x, we need to isolate the variable on the left side of the equation. We will do this by performing the same operations on both sides of the equation.

\displaystyle x-234.67=98.54 

Add \displaystyle 234.67 to both sides of the equation.

\displaystyle x-234.67+234.67=98.54+234.67

Solve.

\displaystyle x=333.21

Example Question #273 : Equations

Solve for \displaystyle x.

\displaystyle x-834.92=-1083.5

Possible Answers:

\displaystyle -238.41

\displaystyle 349.32

\displaystyle 368.64

\displaystyle 128.44

\displaystyle -248.58

Correct answer:

\displaystyle -248.58

Explanation:

In order to solve for \displaystyle x, we need to isolate the variable on the left side of the equation. We will do this by performing the same operations on both sides of the equation.

\displaystyle x-834.92=-1083.5 

Add \displaystyle 834.92 to both sides of the equation.

\displaystyle x-834.92+834.92=-1083.5+834.92

Solve.

\displaystyle x=-248.58

Example Question #623 : Basic Single Variable Algebra

Solve for \displaystyle x.

\displaystyle x-468.94=-268.98

Possible Answers:

\displaystyle 148.26

\displaystyle -280.22

\displaystyle -265.48

\displaystyle 199.96

\displaystyle -368.44

Correct answer:

\displaystyle 199.96

Explanation:

In order to solve for \displaystyle x, we need to isolate the variable on the left side of the equation. We will do this by performing the same operations on both sides of the equation.

\displaystyle x-468.94=-268.98 

Add \displaystyle 468.94 to both sides of the equation.

\displaystyle x-468.94+468.94=-268.98+468.94

Solve.

\displaystyle x=199.96

Example Question #271 : Equations

Solve for \displaystyle x.

\displaystyle x+91.92=132.7

Possible Answers:

\displaystyle -88.48

\displaystyle -78.65

\displaystyle 39.45

\displaystyle -69.45

\displaystyle 40.78

Correct answer:

\displaystyle 40.78

Explanation:

In order to solve for \displaystyle x, we need to isolate the variable on the left side of the equation. We will do this by performing the same operations on both sides of the equation.

\displaystyle x+91.92=132.7 

Subtract \displaystyle 91.92 from both sides of the equation.

\displaystyle x+91.92-91.92=132.7-91.92

Solve.

\displaystyle x=40.78

Example Question #621 : Basic Single Variable Algebra

Solve for \displaystyle x.

\displaystyle 4x=1024

Possible Answers:

\displaystyle 312

\displaystyle 658

\displaystyle 284

\displaystyle 402

\displaystyle 256

Correct answer:

\displaystyle 256

Explanation:

In order to solve for \displaystyle x, we need to isolate the variable on the left side of the equation. We will do this by performing the same operations on both sides of the equation.

\displaystyle 4x=1024 

Divide both sides of the equation by \displaystyle 4.

\displaystyle \frac{4x}{4}=\frac{1024}{4}

Solve.

\displaystyle x=256

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