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Algebra 1 : Systems of Inequalities

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Example Questions

Example Question #31 : Systems Of Inequalities

|4x + 14| > 30

What is a possible valid value of ?

Possible Answers:

Correct answer:

Explanation:

This inequality can be rewritten as:

4x + 14 > 30 OR 4x + 14 < –30

Solve each for x:

4x + 14 > 30; 4x > 16; x > 4

4x + 14 < –30; 4x < –44; x < –11

Therefore, anything between –11 and 4 (inclusive) will not work. Hence, the answer is 7.

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Example Question #32 : Systems Of Inequalities

Solve for .

$5 + 3p \leq 2p + 12$

Possible Answers:

$p\leq\frac{7}{5}$

$p\leq 7$

$p\leq17$

$p\leq \frac{19}{5}$

$p\leq-7$

Correct answer:

$p\leq 7$

Explanation:

First subtract 2p from both sides:

p + 5 < 12.

Then subtract 5 from both sides:

p < 7

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Example Question #3 : How To Find The Solution To An Inequality With Subtraction

Solve the following inequality.

$10x-5\geq7x-2$

Possible Answers:

$x\leq1$

$x\geq1$

$x\geq3$

$x\geq2$

$x\geq5$

Correct answer:

$x\geq1$

Explanation:

Isolate the term with on one side and the constants on the other side.

$10x-5\geq7x-2$

First subtract 7x on both sides and add 5 to both sides.

$3x\geq3$

Next, divide by 3 to solve for x.

$x\geq1$

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Example Question #6 : How To Find The Solution To An Inequality With Subtraction

Solve for :

4x+7>2x-3

Possible Answers:

x>2

x>-2

x<-5

x>-5

x<-2

Correct answer:

x>-5

Explanation:

To solve for the variable we need to isolate the variable on one side of the inequality and all other constants on the other side. In order to do this, perform inverse operations.

First subtracting 7 from both sides we get:

4x>2x-10

Then subtracting 2x from both sides:

2x>-10

Finally divide both sides by 2:

x>-5

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Example Question #7 : How To Find The Solution To An Inequality With Subtraction

x-6 > 8

Find all of the solutions to this inequality.

Possible Answers:

$[14,\infty ]$

$[\infty ,14]$

$(14,\infty)$

$(\infty , 2]$

$[14,\infty )$

Correct answer:

$(14,\infty)$

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 adding six to each side.

Whatever you do to one side you must also do to the other side.

$x-6{\color{Blue} +6} > 8{\color{Blue} +6}$

This gives you:

x> 14

The answer, therefore, is $(14, \infty )$ .

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Example Question #8 : How To Find The Solution To An Inequality With Subtraction

Solve the following inequality: y+10>3

Possible Answers:

y<-7

y>-13

y<-13

y>-7

y<13

Correct answer:

y>-7

Explanation:

In order to isolate the variable, we will need to subtract 10 on both sides of the equation.

y+10-10>3-10

Simplify the left and the right side of the equation.

y>-7

The answer is: y>-7

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Example Question #9 : How To Find The Solution To An Inequality With Subtraction

Solve for x:

$9x+6\geq-2$

Possible Answers:

$x\geq1$

$x\geq \frac{4}{9}$

$x\leq -\frac{8}{9}$

$x\geq -\frac{8}{9}$

$x\leq \frac{4}{9}$

Correct answer:

$x\geq -\frac{8}{9}$

Explanation:

When you are solving for an inequality, it is easiest to treat the inequality sign as an equal sign while you solve for x.

$9x+6\geq-2$

In order to solve for x, you need to get x by itself on one side. The first thing you would need to do is subtract 6 from both sides. That would leave you with $9x\geq-8$ . In order to get x by itself, you need to divide both sides by 9. This would bring you to the answer of $x\geq -\frac{8}{9}$ .

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

Find the solution to the inequality: $9\geq x+18$

Possible Answers:

$x\geq9$

$x\leq27$

$x\leq9$

$x\geq-9$

$x\leq-9$

Correct answer:

$x\leq-9$

Explanation:

In order to isolate the variable, we need to move the 18 to the left side by subtracting 18 on both sides.

$9-18\geq x+18-18$

Simplify both sides.

$-9\geq x$

This indicates that must be less than or equal to negative nine.

Rewrite the inequality so that the is on the left side, and the number is on the right side.

The answer is: $x\leq-9$

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Example Question #12 : How To Find The Solution To An Inequality With Subtraction

Solve the inequality: x+13<-13

Possible Answers:

x<0

x<-26

x>-26

$x\leq0$

x>0

Correct answer:

x<-26

Explanation:

In order to isolate the x-variable, simply subtract 13 from both sides of the inequality.

x+13-13<-13-13

Simplify both sides of the inequality.

x<-26

There is no need to switch the sign.

The answer is: x<-26

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Example Question #33 : Systems Of Inequalities

Solve the inequality: x+30>-25

Possible Answers:

x>5

x>-5

x>-55

x<5

x<55

Correct answer:

x>-55

Explanation:

In order to solve this inequality, we will need to subtract 30 from both sides of the equation.

x+30-30>-25-30

Simplify both sides of the equation.

The answer is: x>-55

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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 #31 : Systems Of Inequalities

Example Question #32 : Systems Of Inequalities

Example Question #3 : How To Find The Solution To An Inequality With Subtraction

Example Question #6 : How To Find The Solution To An Inequality With Subtraction

Example Question #7 : How To Find The Solution To An Inequality With Subtraction

Example Question #8 : How To Find The Solution To An Inequality With Subtraction

Example Question #9 : How To Find The Solution To An Inequality With Subtraction

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

Example Question #12 : How To Find The Solution To An Inequality With Subtraction

Example Question #33 : Systems Of Inequalities

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