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High School Math : Algebraic Equations

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Example Questions

Example Question #4 : How To Do Word Problems Where Two Quantities Are Unknown

Two cars leave a city at the same time. One heads east at $35\: mph$ and the other heads west at $67\: mph$ . How far apart are they after hours?

Possible Answers:

$96\text{ miles}$

$201\text{ miles}$

$105\text{ miles}$

$1.9\text{ miles}$

$306\text{ miles}$

Correct answer:

$306\text{ miles}$

Explanation:

Remember, $\text{distance}={\text{rate}}*{\text{time}}$ . If we look at the car going east, this would mean:

$\text{distance}={\text{rate}}*{\text{time}}$

$\text{distance}=35\: mph*3\text{ hours}$

$\text{distance}=105\text{ miles}$

If we look at the car going west, then:

$\text{distance}={\text{rate}}*{\text{time}}$

$\text{distance}=67\: mph*3\text{ hours}$

$\text{distance}=201\text{ miles}$

Therefore, we need to add the two distances to find the total distance between them.

$T=201\text{ miles}+105 \text{ miles}$

$T=306\text{ miles}$

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Example Question #31 : Algebraic Equations

X+7=45

X=?

Possible Answers:

Correct answer:

Explanation:

To isolate on one side, subtract seven from both sides

$X+7\left- ( 7\right )=45\left- ( 7\right )$

X=45-7=38

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Example Question #2 : How To Solve One Step Equations With Integers In Pre Algebra

3Y=69

Y=?

Possible Answers:

207

Correct answer:

Explanation:

To solve the equation for , you must isolate on one side. Here you can divide both sides by 3.

3Y=6

$\frac{3Y}{3}=\frac{69}{3}$

Y=23

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Example Question #32 : Algebraic Equations

Solve for .

n+5=11

Possible Answers:

n=16

n=15

n=5

n=6

Correct answer:

n=6

Explanation:

To solve equations, you must perform the same operations on both sides.

n+5=11

Subtract 5 from both sides.

n+5-5=11-5

n=6

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Example Question #3 : How To Solve One Step Equations With Integers In Pre Algebra

Solve the following equation for .

-5x = 25

Possible Answers:

$\frac{1}{5}$

Correct answer:

Explanation:

-5x = 25

In order to solve a one step equation, we want to isolate the variable. To do this, we pay special attention to what is being done to the variable. In this case we are multiplying the variable by . To "undo" this, we use the inverse of multiplication, which is division; thus we divide by on both sides. Note that we are dividing by since that is what is being multiplied; don't be tricked into dividing by .

$\frac{-5x}{-5}=\frac{25}{-5}$

x=-5

Dividing both sides by , we get x=-5 .

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Example Question #3 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for if 3x=45 .

Possible Answers:

x=12

x=18

x=15

x=9

Correct answer:

x=15

Explanation:

To solve for we must get all of the numbers on the other side of the equation as .

To do this in a problem where is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is so we divide each side of the equation by to make it look like this $\frac{3x}{3}=\frac{45}{3}$ .

The s cancel to leave by itself.

Then we perform the necessary division to get the answer of x=15 .

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Example Question #2 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for if x-18=24 ?

Possible Answers:

x=6

x=38

x=46

x=42

Correct answer:

x=42

Explanation:

To solve for we must get all of the numbers on the other side of the equation as .

To do this in a problem where is being subtracted by a number, we must add the number to both sides of the equation.

In this case the number is so we add to each side of the equation to make it look like this x-18+18=24+18

The s cancel on the left side and leave by itself.

Then we perform the necessary addition to get the answer of x=42 .

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Example Question #4 : How To Solve One Step Equations With Integers In Pre Algebra

Solve for :

x -5 =20

Possible Answers:

100

Correct answer:

Explanation:

Remembering the final goal is to get the alone on one side of the equation.

To get rid of the , we perform the opposite operation. We add to each side of the equation, cancelling out the on the left side.

This brings the equation to x =25 .

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Example Question #2 : How To Solve One Step Equations With Integers In Pre Algebra

If x=7 what is $x^{{2}}+ 5$ ?

Possible Answers:

Correct answer:

Explanation:

If x=7 you put in for . Therefore it becomes $7^{2}$ .

$7 \times 7= 49$

Finally, 49 +5 =54

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Example Question #1 : How To Solve One Step Equations With Integers In Pre Algebra

Simplify:

$2x^{3} \cdot 2x^{4}$

Possible Answers:

$2x^{12}$

$2x^{7}$

4x^7

$4x^{1}$

$4x^{12}$

Correct answer:

4x^7

Explanation:

First you multiply the coefficients $(2\cdot 2)$ .

Then you multiply $x^{3} \cdot x^4$ According to the laws of exponents, when you multiply two numbers with similar bases (both in this case) then you simply add the exponents (3+4 =7) .

Therefore, the final answer is 4x^7 .

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High School Math : Algebraic Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #4 : How To Do Word Problems Where Two Quantities Are Unknown

Example Question #31 : Algebraic Equations

Example Question #2 : How To Solve One Step Equations With Integers In Pre Algebra

Example Question #32 : Algebraic Equations

Example Question #3 : How To Solve One Step Equations With Integers In Pre Algebra

Example Question #3 : How To Solve One Step Equations With Integers In Pre Algebra

Example Question #2 : How To Solve One Step Equations With Integers In Pre Algebra

Example Question #4 : How To Solve One Step Equations With Integers In Pre Algebra

Example Question #2 : How To Solve One Step Equations With Integers In Pre Algebra

Example Question #1 : How To Solve One Step Equations With Integers In Pre Algebra

All High School Math Resources

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