Studdy AI Logo
Math

QuestionSolve the inequality 3x+3≥x+63x + 3 \geq x + 6 and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. We are given the inequality 3x+3≥x+63x +3 \geq x +6. . We need to solve this inequality for xx.
3. The solution should be written in interval notation.

STEP 2

First, we need to simplify the inequality. We can do this by subtracting xx from both sides of the inequality.
x+−x≥x+6−xx + - x \geq x +6 - x

STEP 3

implify the inequality.
2x+3≥62x +3 \geq6

STEP 4

Next, subtract3 from both sides of the inequality to isolate 2x2x on the left side.
2x+3−3≥6−32x +3 -3 \geq6 -3

STEP 5

implify the inequality.
2x≥32x \geq3

STEP 6

Finally, divide both sides of the inequality by2 to solve for xx.
2x2≥32\frac{2x}{2} \geq \frac{3}{2}

STEP 7

implify to find the solution for xx.
x≥32x \geq \frac{3}{2}This inequality means that xx is greater than or equal to 32\frac{3}{2}.

STEP 8

To write the solution in interval notation, we use a square bracket to indicate that the endpoint is included in the solution set (since xx can be equal to 32\frac{3}{2}), and we use a parenthesis to indicate that the solution set extends to infinity.
x∈[32,∞)x \in \left[\frac{3}{2}, \infty\right)So, the solution to the inequality 3x+3≥x+63x +3 \geq x +6 is x∈[32,∞)x \in \left[\frac{3}{2}, \infty\right).

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