Problem

Solve the inequality 2x−3>5 and 3x+2<14 and express the solution as a single interval.

Answer

Expert–verified
Hide Steps
Answer

Since we want the solution that satisfies both inequalities, we need to find the intersection of the intervals x>4 and x<4. However, there is no value of x that is both greater than and less than 4, so the intersection is the empty set.

Steps

Step 1 ：First solve the inequality 2x−3>5. Add 3 to both sides to get 2x>8, then divide by 2 to get x>4.

Step 2 ：Next solve the inequality 3x+2<14. Subtract 2 from both sides to get 3x<12, then divide by 3 to get x<4.

Step 3 ：Since we want the solution that satisfies both inequalities, we need to find the intersection of the intervals x>4 and x<4. However, there is no value of x that is both greater than and less than 4, so the intersection is the empty set.

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find y′ if $y=\ln \… 3. (3pts) Cherry trees in a c… More