Studdy AI Logo
Math

Question Solve for xx in the inequality 3x−7>7x+93x - 7 > 7x + 9 and graph the solution.

Studdy Solution

STEP 1

Assumptions
1. We are given an inequality 3x−7>7x+93x - 7 > 7x + 9.
2. We need to solve for xx.
3. After finding the solution for xx, we will graph the solution on a number line.

STEP 2

Start by isolating the variable xx on one side of the inequality. We can do this by subtracting 7x7x from both sides of the inequality.
3x−7x−7>7x−7x+93x - 7x - 7 > 7x - 7x + 9

STEP 3

Simplify the terms on both sides of the inequality.
−4x−7>9-4x - 7 > 9

STEP 4

Next, we will isolate xx by adding 77 to both sides of the inequality.
−4x−7+7>9+7-4x - 7 + 7 > 9 + 7

STEP 5

Simplify the terms on both sides of the inequality.
−4x>16-4x > 16

STEP 6

To solve for xx, we need to divide both sides of the inequality by −4-4. Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the direction of the inequality.
−4x−4<16−4\frac{-4x}{-4} < \frac{16}{-4}

STEP 7

Simplify both sides of the inequality to find the solution for xx.
x<−4x < -4

STEP 8

Now that we have the solution for xx, we can graph it on a number line. To graph x<−4x < -4, we draw a number line, place a point at −4-4, and shade the region to the left of −4-4 to indicate that xx can be any number less than −4-4.
The solution to the inequality 3x−7>7x+93x - 7 > 7x + 9 is x<−4x < -4.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord