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Algebra 1 : Systems of Inequalities

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Example Questions

Example Question #2222 : Algebra 1

Solve for :

3x-1< x+5

Possible Answers:

x>1

x>3

x<3

x<1

None of the other answers are correct.

Correct answer:

x<3

Explanation:

To solve this inequality, get the 's to one side of the equation and the integers to the other side.

Add 1 to both sides:

2x<6

Divide both sides by 2:

x<3

(Since we are not dividing by a negative number, there is no need to reverse the sign.)

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Example Question #2231 : Algebra 1

Find the solution set to the compound inequality:

$\left ( 5y+19< 74 \right )\bigcap \left ( -3y+13> 40 \right )$

Possible Answers:

$\left ( -\infty , -9\right )$

$\left ( -\infty , \infty \right )$

$(-\infty ,11)$

$(-\infty ,-9) \cup (11, \infty )$

(-9,11)

Correct answer:

$\left ( -\infty , -9\right )$

Explanation:

Solve each of these two inequalities separately:

5y + 19 < 74

5y + 19 -19 < 74 -19

5y < 55

$5y \div 5 < 55 \div 5$

y < 11 , or in interval form, $\left ( -\infty , 11\right )$

-3y + 13 > 40

-3y + 13 - 13 > 40- 13

-3y > 27

$-3y \div (-3) < 27 \div (-3)$

(Note the flipping of the inequality because of the division by a negative number.)

y < -9 , or in interval form, $\left ( -\infty , -9\right )$

The question asks about the intersection of the two intervals:

$\left ( -\infty , 11\right ) \cap \left ( -\infty , -9\right )$

The intersection is the area of the number line that the two sets share, or $\left ( -\infty , -9\right )$ .

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Example Question #18 : How To Find The Solution To An Inequality With Division

Solve the following inequality.

5x+4 > x-4

Possible Answers:

x<3

x>-2

x>4

x>5

x>2

Correct answer:

x>-2

Explanation:

To solve this inequality, move all the terms with on one side and all other terms on the other side, then solve for x.

5x+4 > x-4

4x>-8

x>-2

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Example Question #19 : How To Find The Solution To An Inequality With Division

Solve the inequality

2x+9> -x+1 .

Possible Answers:

$x>-\frac{8}{3}\:$

$x<\frac{8}{3}\:$

$x>-\frac{3}{8}\:$

$x>\frac{8}{3}\:$

$x<-\frac{8}{3}\:$

Correct answer:

$x>-\frac{8}{3}\:$

Explanation:

Inequalities are treated as equalities when it comes to balancing, with the exception of division by a negative number (then flip the greater/less than symbol).

The question is asking for the solved inequality isolating . Combine like terms across sides by adding or subtracting same value to both sides.

2x+9> -x+1

2x>-x-8

3x>-8

$x>-\frac{8}{3}$

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Example Question #20 : How To Find The Solution To An Inequality With Division

Solve the inequality.

$4x+3\geq -4$

Possible Answers:

$x\leq -\frac{7}{4}$

$x> \frac{3}{4}$

$x> -\frac{7}{4}$

$x\geq -\frac{7}{4}$

$x> \frac{7}{4}$

Correct answer:

$x\geq -\frac{7}{4}$

Explanation:

Use the properties of inequalities to balance the inequality and isolate .

$4x+3\geq -4$

First subtract three from both sides.

$4x\geq -7$

Next, divide by four.

$x\geq -\frac{7}{4}$

Since no division or multiplication of a negative number occurred, the inequality sign remains the same.

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Example Question #2232 : Algebra 1

Simplify the following inequality:

-3x>6

Possible Answers:

x<-2

$x\geq-2$

$x\leq-2$

x>-2

Correct answer:

x<-2

Explanation:

To do this question all you need to do is divide both sides by

So, $\frac{-3x}{-3}> \frac{6}{-3}$

Which gives you: x<-2

It is important to remember that the greater than sign flips to less than when dividing by a negative number.

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Example Question #22 : How To Find The Solution To An Inequality With Division

Solve the following inequality for :

4x+3<2x-13

Possible Answers:

x<-5

x<8

x>8

x>5

x<-8

Correct answer:

x<-8

Explanation:

4x+3<2x-13

First, using the additive inverses, isolate the variables and constants on either side of the equation. In other words, subtract from both sides, and subtract from both sides. This leaves you with:

2x<-16

Now use the multiplicative inverse (divide by ) to solve the inequality.

Keep in mind that we do not flip the inequality symbol because the number we were dividing by is positive.

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Example Question #104 : Equations / Inequalities

$\frac{x}{4}<7$

Find all of the solutions to this inequality.

Possible Answers:

[0,7]

$(-\infty , 28)$

$[\infty ,28]$

$[-\infty , 28)$

$(\infty, 7)$

Correct answer:

$(-\infty , 28)$

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 multiplying each side by four.

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

${\color{Blue} 4}(\frac{x}{4})<(7){\color{Blue} 4}$

This gives you:

x<28

The answer, therefore, is $(-\infty , 28)$ .

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Example Question #105 : Equations / Inequalities

Solve the following inequality: -2x+4>0

Possible Answers:

x>2

x<8

x<-2

x<2

x>-2

Correct answer:

x<2

Explanation:

To isolate the variable, first subtract four on both sides.

-2x+4-4>0-4

Simplify the left and the right side of the equation.

-2x>-4

Divide by negative two on both sides. When dividing by a negative number, be sure to switch the sign.

$\frac{-2x}{-2}<\frac{-4}{-2}$

x<2

The answer is: x<2

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Example Question #2233 : Algebra 1

Solve: -2x>12

Possible Answers:

x>-6

$x\leq-6$

x<-6

$x\geq-6$

x<6

Correct answer:

x<-6

Explanation:

Divide by negative two on both sides. When dividing a negative number, switch the sign of the inequality.

$\frac{-2x}{-2}>\frac{12}{-2}$

Simplify both sides of the equation.

The answer is: x<-6

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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 #2222 : Algebra 1

Example Question #2231 : Algebra 1

Example Question #18 : How To Find The Solution To An Inequality With Division

Example Question #19 : How To Find The Solution To An Inequality With Division

Example Question #20 : How To Find The Solution To An Inequality With Division

Example Question #2232 : Algebra 1

Example Question #22 : How To Find The Solution To An Inequality With Division

Example Question #104 : Equations / Inequalities

Example Question #105 : Equations / Inequalities

Example Question #2233 : Algebra 1

All Algebra 1 Resources

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