How to find the solution to an inequality with division - Algebra

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Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

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Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Compare your answer with the correct one above

Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Compare your answer with the correct one above

Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Compare your answer with the correct one above

Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Compare your answer with the correct one above

Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Compare your answer with the correct one above

Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Compare your answer with the correct one above

Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

Compare your answer with the correct one above

Question

Find the solution set for the inequality.

Answer

Subtract 100 from each side:

Divide both sides by -2:

(Note that the inequality symbol switched when we divided by a negative number.)

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Question

Solve for :

Answer

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:

Divide both sides by 2:

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

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Question

Solve for :

Answer

To solve for , separate the integers and 's by adding 1 and subtracting from both sides to get . Then, divide both sides by 2 to get . Since you didn't divide by a negative number, the sign does not need to be reversed.

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Question

Solve for :

Answer

First, add and subtract from both sides of the inequality to get .

Then, divide both sides by and reverse the sign since you are dividing by a negative number.

This gives you .

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Question

Solve the following:

Answer

$\frac{-2x}{-2}<\frac{1}{-2}$ Don't forget to change the direction of the inequality sign when dividing by a negative number!

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

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Question

Give the solution set of the inequality:

$-5x + 17 \geq 82$

Answer

$-5x + 17 \geq 82$

$-5x + 17 -17 \geq 82-17$

$-5x \geq 65$

$-5x \div (-5) \leq 65\div (-5)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$x \leq -13$

or, in interval form,

$(-\infty , -13]$

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Question

Give the solution set of the inequality:

$-5x + 27 \leq 62$

Answer

$-5x + 27 \leq 62$

$-5x + 27 -27 \leq 62-27$

$-5x \leq 35$

$-5x \div (-5) \leq 35\div (-5)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

$x \geq -7$

or, in interval form,

$[-7,\infty )$

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Question

Give the solution set of the inequality:

Answer

$-4x \div (-4) > 56 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

$(-14, \infty )$

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Question

Give the solution set of the inequality:

Answer

$-4x \div (-4)< 64 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

$(-\infty ,-16)$

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Question

Give the solution set of the inequality:

Answer

$-4x \div (-4) > 68 \div (-4)$

Note change in direction of the inequality symbol when the expressions are divided by a negative number.

or, in interval form,

$(-17,\infty )$

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Question

Find the solution set to the compound inequality:

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

Answer

Solve each of these two inequalities separately:

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

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

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

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

, 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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Question

Find the solution set to the following compound inequality statement:

$4y + 15 < 91 \textrm{ and } 7y -12 > 86$

Answer

Solve each of these two inequalities separately:

$4y \div 4 < 76 \div 4$

, or, in interval form, $(-\infty , 19)$

$7y \div 7 > 98 \div 7$

, or, in interval form, $(14, \infty )$

The two inequalities are connected with an "and", so we take the intersection of the two intervals.

$(14, \infty ) \cap (-\infty , 19) = (14,19)$

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