Solved on Jan 19, 2024

Find the number $x$ such that $-3x - 5 > 125$ . Which inequality represents the solution set for $x$ ?

STEP 1

Assumptions
1. Let the unknown number be represented by the variable $x$ .
2. The phrase "the difference of -3 times a number and -5" can be represented algebraically as $-3x - (-5)$ .
3. The inequality states that this difference is greater than 125.

STEP 2

Write the inequality as described by the problem statement.
$-3x - (-5) > 125$

STEP 3

Simplify the left side of the inequality by removing the parentheses, keeping in mind that subtracting a negative is the same as adding a positive.
$-3x + 5 > 125$

STEP 4

Subtract 5 from both sides of the inequality to isolate the term involving $x$ on one side.
$-3x + 5 - 5 > 125 - 5$

STEP 5

Simplify both sides of the inequality.
$-3x > 120$

STEP 6

Divide both sides of the inequality by -3 to solve for $x$ . Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
$\frac{-3x}{-3} < \frac{120}{-3}$

STEP 7

Solve for $x$ .
$x < -40$

STEP 8

Now, we need to match our inequality $x < -40$ with the correct answer choice from A, B, C, or D.
The inequality that represents the solution set for the number is $x < -40$ .

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Find the number $x$ such that $-3x - 5 > 125$ . Which inequality represents the solution set for $x$ ?

STEP 1

Assumptions
1. Let the unknown number be represented by the variable $x$ .
2. The phrase "the difference of -3 times a number and -5" can be represented algebraically as $-3x - (-5)$ .
3. The inequality states that this difference is greater than 125.

STEP 2

Write the inequality as described by the problem statement.
$-3x - (-5) > 125$

STEP 3

Simplify the left side of the inequality by removing the parentheses, keeping in mind that subtracting a negative is the same as adding a positive.
$-3x + 5 > 125$

STEP 4

Subtract 5 from both sides of the inequality to isolate the term involving $x$ on one side.
$-3x + 5 - 5 > 125 - 5$

STEP 5

Simplify both sides of the inequality.
$-3x > 120$

STEP 6

Divide both sides of the inequality by -3 to solve for $x$ . Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
$\frac{-3x}{-3} < \frac{120}{-3}$

STEP 7

Solve for $x$ .
$x < -40$

STEP 8

Now, we need to match our inequality $x < -40$ with the correct answer choice from A, B, C, or D.
The inequality that represents the solution set for the number is $x < -40$ .

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Find the number xxx such that −3x−5>125-3x - 5 > 125−3x−5>125. Which inequality represents the solution set for xxx?

STEP 1

Assumptions1. Let the unknown number be represented by the variable xxx.2. The phrase "the difference of -3 times a number and -5" can be represented algebraically as −3x−(−5)-3x - (-5)−3x−(−5).3. The inequality states that this difference is greater than 125.

STEP 2

Write the inequality as described by the problem statement.−3x−(−5)>125-3x - (-5) > 125−3x−(−5)>125

STEP 3

Simplify the left side of the inequality by removing the parentheses, keeping in mind that subtracting a negative is the same as adding a positive.−3x+5>125-3x + 5 > 125−3x+5>125

STEP 4

Subtract 5 from both sides of the inequality to isolate the term involving xxx on one side.−3x+5−5>125−5-3x + 5 - 5 > 125 - 5−3x+5−5>125−5

STEP 5

Simplify both sides of the inequality.−3x>120-3x > 120−3x>120

STEP 6

Divide both sides of the inequality by -3 to solve for xxx. Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.−3x−3<120−3\frac{-3x}{-3} < \frac{120}{-3}−3−3x​<−3120​

STEP 7

Solve for xxx.x<−40x < -40x<−40

STEP 8

Now, we need to match our inequality x<−40x < -40x<−40 with the correct answer choice from A, B, C, or D.The inequality that represents the solution set for the number is x<−40x < -40x<−40.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the number $x$ such that $-3x - 5 > 125$ . Which inequality represents the solution set for $x$ ?

Assumptions
1. Let the unknown number be represented by the variable $x$ .
2. The phrase "the difference of -3 times a number and -5" can be represented algebraically as $-3x - (-5)$ .
3. The inequality states that this difference is greater than 125.

Write the inequality as described by the problem statement.
$-3x - (-5) > 125$

Simplify the left side of the inequality by removing the parentheses, keeping in mind that subtracting a negative is the same as adding a positive.
$-3x + 5 > 125$

Subtract 5 from both sides of the inequality to isolate the term involving $x$ on one side.
$-3x + 5 - 5 > 125 - 5$

Simplify both sides of the inequality.
$-3x > 120$

Divide both sides of the inequality by -3 to solve for $x$ . Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
$\frac{-3x}{-3} < \frac{120}{-3}$

Solve for $x$ .
$x < -40$

Now, we need to match our inequality $x < -40$ with the correct answer choice from A, B, C, or D.
The inequality that represents the solution set for the number is $x < -40$ .