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Algebra 1 : Systems of Inequalities

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Example Question #61 : Systems Of Inequalities

Solve this inequality:

$12x-5\geq-4x+43$

Possible Answers:

$x\geq2$

$x\geq3$

Not enough information to be determined.

$x\geq6$

$x\geq4$

Correct answer:

$x\geq3$

Explanation:

To solve this inequality, we need to separate the constants from the variables so that they are on opposite sides of the inequality.

We can do this by adding (4x+5) to each side and

$12x-5+(4x+5)\geq-4x+43 + (4x+5)$ .

The constants cancel on the left side, and the variables cancel on the right side.

$16x+0\geq0x+48$

$16x\geq48$

Then, we divide both sides by 16, to get our final answer:

$\frac{16x}{16}\geq\frac{48}{16}$

$x\geq 3$

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Example Question #61 : Systems Of Inequalities

Simplify the following inequality:

$x-8 \geq 15$

Possible Answers:

$x\geq 23$

$x\leq23$

$x\geq -23$

$x\geq7$

Correct answer:

$x\geq 23$

Explanation:

This is a one-step problem in which all you need to do is add the to both sides to get by itself.

So, $x-8+8\geq 15+8$

Then simplify to get:

$x\geq23$

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Example Question #2192 : Algebra 1

x+3>4

Find all of the solutions to this inequality.

Possible Answers:

[0,1]

$[1,\infty )$

$(1,\infty )$

(1,0]

$[1,\infty ]$

Correct answer:

$(1,\infty )$

Explanation:

To solve an inequality, isolate the variable on one side with all other constants on the other side. To accomplish this, perform opposite operations to manipulate the inequality.

First, isolate the x by subtracting three from each side.

Whatever operation you do to one side you must do to the other side as well.

$x+3{\color{Blue} -3}>4{\color{Blue} -3}$

This gives you:

x>1

The answer, therefore, is $(1,\infty )$ .

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Example Question #11 : How To Find The Solution To An Inequality With Addition

Solve the inequality: x-9>9

Possible Answers:

x>-18

x<18

x>18

x<0

x>0

Correct answer:

x>18

Explanation:

In order to isolate the variable, we will need to add nine on both sides.

x-9+9 > 9+9

Simplify both sides of the equation.

x>18

The answer is x>18 .

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Example Question #2194 : Algebra 1

Solve the following inequality: x-4 >36

Possible Answers:

x>40

x<-40

x<32

x>-40

x>32

Correct answer:

x>40

Explanation:

Add both sides by four to isolate the variable.

x-4+4 >36+4

Simplify both sides of the equation.

The answer is: x>40

This means that is greater than forty, but cannot equal to forty.

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Example Question #61 : Systems Of Inequalities

Solve for x in the following inequality:

$x - 5 \geq 9$

Possible Answers:

$x \geq 14$

$x \leq 4$

x = 14

$x \leq 14$

$x \geq 4$

Correct answer:

$x \geq 14$

Explanation:

When solving an inequality, we will solve it the same way we would solve an equation. We are solving for x, so we want x to stand alone. In the equation

$x - 5 \geq 9$

we want to add 5 to both sides. The inequality symbol does not change. We get

$x - 5 + 5 \geq 9 + 5$

$x \geq 14$

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Example Question #62 : Systems Of Inequalities

Find the solution of the inequality: x-14>9

Possible Answers:

x>23

x=23

x<23

$x\geq23$

$x\leq23$

Correct answer:

x>23

Explanation:

To isolate the unknown variable, we will need to add 14 on both sides.

x-14+14>9+14

Simplify both sides of the equation.

The answer is: x>23

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Example Question #63 : Systems Of Inequalities

Solve the inequality: x-12>23

Possible Answers:

$x\geq35$

$x\leq 35$

x<35

x>11

x>35

Correct answer:

x>35

Explanation:

In order to solve for the unknown variable, add 12 on both sides.

x-12+(12)>23+(12)

Simplify both sides.

The answer is: x>35

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Example Question #2198 : Algebra 1

Find the solution: 3-x<0

Possible Answers:

x<-3

x>-3

x>3

x<3

x=3

Correct answer:

x>3

Explanation:

To solve this inequality, simply add the variable on both sides. This method eliminates having to divide by negative one on both sides and switch the sign.

3-x+(x)<0+(x)

3<x

This inequality is the same as x>3 since the unknown variable must be greater than three.

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Example Question #61 : Systems Of Inequalities

Solve the following inequality: -6+x-3>1

Possible Answers:

x<-8

x<2

x>-8

x>10

x<10

Correct answer:

x>10

Explanation:

In order to solve this inequality, we must add six and three on both sides of the inequality to isolate the x-variable.

-6+x-3 + (3+6)>1+ (3+6)

This will cancel out the terms and leave x by itself on the left side.

The answer is: x>10

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Algebra 1 : Systems of Inequalities

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #61 : Systems Of Inequalities

Example Question #61 : Systems Of Inequalities

Example Question #2192 : Algebra 1

Example Question #11 : How To Find The Solution To An Inequality With Addition

Example Question #2194 : Algebra 1

Example Question #61 : Systems Of Inequalities

Example Question #62 : Systems Of Inequalities

Example Question #63 : Systems Of Inequalities

Example Question #2198 : Algebra 1

Example Question #61 : Systems Of Inequalities

All Algebra 1 Resources

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