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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Solving Inequalities

Solve for :

x^2+4x>12

Possible Answers:

x<-12

x<6

$x<-6\ and\ x>2$

$x<-2\ and\ x>6$

x>2

Correct answer:

$x<-6\ and\ x>2$

Explanation:

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that becomes , and vice versa. When we solve binomials, we must take extra caution because (-x)^2=x^2 .

So when we solve inequalities with binomials, we must create two scenarios: one where the value inside of the parentheses is positive and one where it is negative. For the negative scenario, we must flip the sign as we normally do for inequalities.

x^2+4x>12

x^2+4x+4>12+4

(x+2)^2>16

Now we must create our two scenarios:

$x+2>{\sqrt{16}}$ and $x+2<-{\sqrt{16}}$

Notice that in the negative scenario, we flipped the sign of the inequality.

x+2>4 and x+2<-4

x>2 and x<-6

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Example Question #2 : Solving Inequalities

Solve for :

x^2-10x<24

Possible Answers:

x<-12

$x>-2\ and\ x<12$

$x>0\ and\ x<2$

x>5

$x<5\ and\ x>10$

Correct answer:

$x>-2\ and\ x<12$

Explanation:

x^2-10x<24

x^2-10x+25<24+25

(x-5)^2<49

Now we must create our two scenarios:

$x-5<{\sqrt{49}}$ and $x-5>-{\sqrt{49}}$

Notice that in the negative scenario, we flipped the sign of the inequality.

x-5<7 and x-5>-7

x<12 and x>-2

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Example Question #1 : Solving Inequalities

Solve the inequality for x:

2x+4>64

Possible Answers:

x>28

x<28

x<30

x>30

x=30

Correct answer:

x>30

Explanation:

2x+4>64

Subtract 4 from both sides:

2x > 60

Divide both sides by 2:

x > 30

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Example Question #2073 : Algebra Ii

Solve for .

$-7x-4\geq10$

Possible Answers:

$x\leq2$

$x\geq2$

$x\leq-2$

$x\geq-2$

Correct answer:

$x\leq-2$

Explanation:

$-7x-4\geq10$

Add 4 to both sides.

$-7x\geq14$

Divide both sides by –7. When dividing by a negative value, we must also change the direction of the inequality sign.

$x\leq-2$

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Example Question #3 : Solving Inequalities

Solve for :

$9x-27\geq6x$

Possible Answers:

$x\geq9$

x>9

$x\leq3$

$x\leq9$

$x\geq3$

Correct answer:

$x\geq9$

Explanation:

$9x-27\geq6x$

Move like terms to the same sides:

$9x-6x\geq27$

Combine like terms:

$3x\geq27$

Divide both sides by 3:

$x\geq9$

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Example Question #11 : Solving Inequalities

Solve for :

$5-3x\leq14$

Possible Answers:

$x\leq3$

$x\geq-3$

$x\geq9$

$x\geq0$

$x\geq3$

Correct answer:

$x\geq-3$

Explanation:

$5-3x\leq14$

$-3x\leq9$

$\frac{-3x}{-3}\geq\frac{9}{-3}$

$x\geq-3$

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Example Question #1531 : High School Math

Sarah notices her map has a scale of $\frac{1}{4}\; in=1\; mile$ . She measures $12.5\; in$ between Beaver Falls and Chipmonk Cove. How far apart are the cities?

Possible Answers:

$25\; miles$

$50\; miles$

$60\; miles$

$75\; miles$

$90\; miles$

Correct answer:

$50\; miles$

Explanation:

$\frac{1}{4}\; in=1\; mile$ is the same as $1\; in = 4\; miles$

So to find out the distance between the cities

$12.5\; in \cdot \frac{4\; miles}{1\;in }=50\; miles$

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Example Question #1 : Other Mathematical Relationships

Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?

(1 gallon = 4 quarts)

Possible Answers:

$1.50\; gallons$

$1.75\; gallons$

$1.00\; gallons$

$0.75\; gallons$

$0.50\; gallons$

Correct answer:

$1.50\; gallons$

Explanation:

First set up the proportion:

$\frac{3\; parts \; yellow}{1 \; part\; red}=\frac{x \; quarts \; yellow}{2 \; quarts \; red}$

x = $6 \; quarts\;yellow\; paint$

Then convert this to gallons:

$6 \; quarts\; \cdot \frac{1 \; gallon}{4\; quarts}= 1.50\; gallons$

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Example Question #246 : Algebra Ii

If is directly proportional to , and x=2 when y=8 , find a formula for .

Possible Answers:

y=8x

$y=\frac{x}{4}$

y=4x

$\frac{y}{4}=x$

y=2x

Correct answer:

y=4x

Explanation:

8=k*2 since x=2 and y=8

Solving for , you get that k=4

Replacing in the original equation, you get the answer of

y=4x

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Example Question #243 : Algebra Ii

If is inversely proportional to , and if x=2 when y=8 , find a formula for .

Possible Answers:

y=16x

$y=\frac{x}{16}$

y=4x

$y=\frac{16}{x}$

$\frac{16}{y}=x$

Correct answer:

$y=\frac{16}{x}$

Explanation:

Since y is inversely porportional to x, you can use the standard equations of $y=\frac{k}{x}$ where k is a constant. Plugging the given x and y into this equation to solve for k, k=16 . To get the answer, substitute k into the standard equation.

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All High School Math Resources

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Solving Inequalities

Example Question #2 : Solving Inequalities

Example Question #1 : Solving Inequalities

Example Question #2073 : Algebra Ii

Example Question #3 : Solving Inequalities

Example Question #11 : Solving Inequalities

Example Question #1531 : High School Math

Example Question #1 : Other Mathematical Relationships

Example Question #246 : Algebra Ii

Example Question #243 : Algebra Ii

All High School Math Resources

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