Problem 37
Question
Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$2 x-11<-3(x+2)$$
Step-by-Step Solution
Verified Answer
The solution to the inequality \(2x - 11 < -3(x + 2)\) is \(x < 1\), represented in interval notation as \(-\infty, 1)\).
1Step 1: Solving the linear inequality
Firstly simplify the inequality by removing parentheses: \(2x - 11 < -3x -6\). Secondly, add 3x to both sides of the inequality to isolate the term with x in one side of the inequality: \(5x - 11 < -6\). Thirdly, add 11 to both sides of the inequality to isolate x: \(5x < 5\). Lastly, divide both sides by 5 to solve for x: \(x < 1 \)
2Step 2: Writing the solution in interval notation
The interval notation for \(x < 1\) is \(-\infty, 1)\). The parentheses indicates that 1 is not included in the solution.
3Step 3: Graphing the solution on a number line
To graph \(x < 1\) on the number line, make an open circle at 1 (since 1 is not included in the solution), and draw an arrow to the left (since \(x < 1\)).
Other exercises in this chapter
Problem 37
In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ \frac{-8+\sqrt{-32}}{24} $$
View solution Problem 37
In Exercises \(35-46,\) determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the tri
View solution Problem 37
Solve each equation with rational exponents. Check all proposed solutions. $$ (x-4)^{\frac{2}{3}}=16 $$
View solution Problem 37
Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These a
View solution