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Algebra 1 : Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #37 : How To Find The Solution To An Inequality With Division

Solve the inequality: $-2x>-\frac{1}{3}$

Possible Answers:

$x<-\frac{1}{6}$

$x<\frac{2}{3}$

$x>\frac{1}{6}$

$x<\frac{1}{6}$

$x<-\frac{2}{3}$

Correct answer:

$x<\frac{1}{6}$

Explanation:

Divide both sides by negative two. We will need to switch the direction of the sign.

$\frac{-2x}{-2}>\frac{-\frac{1}{3}}{-2}$

Simplify both sides and switch the sign. Rewrite the complex fraction such that dividing by a negative two is similar to multiplying by negative half.

$x< -\frac{1}{3} \cdot -\frac{1}{2}$

Multiply the fractions on the right.

The answer is: $x<\frac{1}{6}$

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Example Question #38 : How To Find The Solution To An Inequality With Division

Solve the inequality: $-\frac{1}{8}x>8$

Possible Answers:

$x>\frac{63}{8}$

x>-64

x<-1

$x\leq-64$

x<-64

Correct answer:

x<-64

Explanation:

Dividing by negative one-eighth is similar to multiplying by negative eight on both sides. Since we are dividing by a negative number, the sign will switch.

$-\frac{1}{8}x \cdot -8>8 \cdot -8$

Simplify both sides.

The answer is: x<-64

Dividing by negative one-eighth is similar to multiplying by negative eight on both sides. Since we are dividing by a negative number, the sign will switch.

$-\frac{1}{8}x \cdot -8>8 \cdot -8$

Simplify both sides.

The answer is: x<-64

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Example Question #2 : Solving Equations And Inequallities

Solve for :

8x-5-4x=-x+10

Possible Answers:

Correct answer:

Explanation:

8x-5-4x=-x+10 can be simplified to become

4x-5=-x+10

Then, you can further simplify by adding 5 and to both sides to get 5x=15 .

Then, you can divide both sides by 5 to get x=3 .

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Example Question #1 : How To Find The Solution To An Equation

What number is six less than eight more than one half of four times the square of the greatest negative integer?

Possible Answers:

$\frac{1}{3}$

Correct answer:

Explanation:

Turn the word problem into math. Start at the end--what is the greatest negative integer? -1!

$(-1)^2\cdot4\cdot\frac{1}{2}+8-6=1\cdot4\cdot\frac{1}{2}+8-6=2+8-6=4$

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Example Question #1 : How To Find The Solution To An Equation

$18\div\frac{1}{6}\cdot\frac{9}{72}\cdot\frac{4}{27}\cdot(-8+7)^9=$

Possible Answers:

Correct answer:

Explanation:

$18\div\frac{1}{6}\cdot\frac{9}{72}\cdot\frac{4}{27}\cdot(-8+7)^9=18\cdot6\cdot\frac{1}{8}\cdot\frac{4}{27}\cdot-1$

Remember to cancel as you go--the 18 will cancel with the 27, the 4 will cancel with the 8, and so on:

$18\cdot6\cdot\frac{1}{8}\cdot\frac{4}{27}\cdot-1= 2\cdot6\cdot\frac{1}{2}\cdot\frac{1}{3}\cdot-1$

Continue to reduce:

$2\cdot6\cdot\frac{1}{2}\cdot\frac{1}{3}\cdot-1= 2\cdot1\cdot-1=-2$

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Example Question #1 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

6x-1=12x+8-3x

Possible Answers:

Correct answer:

Explanation:

To solve for , you must first combine the 's on the right side of the equation. This will give you $\ 6x-1=9x+8$ .

Then, subtract and from both sides of the equation to get -9=3x .

Finally, divide both sides by to get the solution x=-3 .

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Example Question #1 : How To Find The Solution To An Equation

Solve for :

3x+5=2(3x-2)

Possible Answers:

Correct answer:

Explanation:

First, use the distributive property to simplify the right side of the equation: 3x+5=6x-4 . Then, subtract and add 4 to both sides to separate the 's and the integers to get 9=3x . Divide both sides by 3 to get x=3 .

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Example Question #1 : Systems Of Equations

Solve for :

a(x+b)= c

Possible Answers:

$\frac{c-b}{a}$

$\frac{a-b}{c}$

$\frac{c}{a}-b$

$\frac{a}{c}-b$

$\frac{a}{c-b}$

Correct answer:

$\frac{c}{a}-b$

Explanation:

To solve for , first divide both sides by : $x+b=\frac{c}{a}$ . Then, subtract both sides by to get $x=\frac{c}{a}-b$ .

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Example Question #2 : How To Find The Solution To An Equation

(4^2)^x=64

Possible Answers:

$-\frac{3}{4}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

$(4^2)^x= 4^{2x}=64$

$64= 4\cdot 4\cdot 4=4^3$

$4^{2x}=4^3$

2x = 3

$x = \frac{3}2{}$

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Example Question #1 : How To Find The Solution To An Equation

$\frac{4^2+6\cdot 9}{4+3(2)}+\frac{7}{14}\cdot\frac{50}{25}-1=$

Possible Answers:

19.8

Correct answer:

Explanation:

1. First simplify the first expression:

$\frac{4^2 +6\cdot 9}{4+3(2)}=\frac{4\cdot 4+54}{4+6}=\frac{16+54}{10}=\frac{70}{10}=7$

2. Then, simplify the next two expressions:

$\frac{7}{14}\cdot\frac{50}{25}=\frac{1}{2}\cdot\frac{2}{1}=1$

3. Finally, add and subtract:

7+1-1=7

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #37 : How To Find The Solution To An Inequality With Division

Example Question #38 : How To Find The Solution To An Inequality With Division

Example Question #2 : Solving Equations And Inequallities

Example Question #1 : How To Find The Solution To An Equation

Example Question #1 : How To Find The Solution To An Equation

Example Question #1 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Example Question #1 : How To Find The Solution To An Equation

Example Question #1 : Systems Of Equations

Example Question #2 : How To Find The Solution To An Equation

Example Question #1 : How To Find The Solution To An Equation

All Algebra 1 Resources

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