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Algebra 1 : Equations / Inequalities

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Example Questions

Example Question #36 : How To Find The Solution To An Inequality With Division

Solve the following inequality: -12x<-36

Possible Answers:

x>3

x<-3

x<3

x>-3

$x\leq3$

Correct answer:

x>3

Explanation:

Divide by negative twelve on both sides of the inequality.

Dividing by a negative value requires changing the direction of the sign.

$\frac{-12x}{-12}<\frac{-36}{-12}$

Simplify both sides.

The answer is: x>3

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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 #1 : How To Find The Solution To An Equation

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 #2 : Systems Of Equations

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 #3 : Systems Of Equations

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

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 #4 : Systems Of Equations

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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Algebra 1 : Equations / Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #36 : How To Find The Solution To An Inequality With Division

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 #1 : How To Find The Solution To An Equation

Example Question #2 : Systems Of Equations

Example Question #3 : Systems Of Equations

Example Question #4 : Systems Of Equations

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

All Algebra 1 Resources

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