Problem 33
Question
Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$8 x-11 \leq 3 x-13$$
Step-by-Step Solution
Verified Answer
The solution to the inequality is \(x \leq -0.4\). In interval notation, this is expressed as \[(-\infty, -0.4]\]. The graph should be shaded to the left of -0.4, inclusively.
1Step 1: Combine like terms
Subtract \(3x\) from both sides to collect all the terms containing x on one side: \[8x - 3x \leq 3x - 3x -13\] which simplifies to, \[5x - 11 \leq -13\]
2Step 2: Isolate the x term
Add 11 to both sides to isolate the x term: \(5x - 11 + 11 \leq -13 + 11\) which simplifies to, \[5x \leq -2\]
3Step 3: Solve for x
Divide both sides by 5 to solve for x: \(5x/5 \leq -2/5\), thus, \[x \leq -0.4\]
4Step 4: Write the solution in interval notation
The solution in interval notation is \[(-\infty, -0.4]\] inclusive of -0.4.
5Step 5: Graph the solution set
On the number line, shade all the numbers less than or equal to -0.4, and indicate -0.4 with a closed circle to show that -0.4 is included in the solution.
Other exercises in this chapter
Problem 33
In Exercises \(29-44\), perform the indicated operations and write the result in standard form. $$ (-2+\sqrt{-4})^{2} $$
View solution Problem 33
Solve each equation in Exercises \(15-34\) by the square root property. $$ (3 x-4)^{2}=8 $$
View solution Problem 33
Solve each equation with rational exponents. Check all proposed solutions. $$(x-4)^{\frac{3}{2}}=27$$
View solution Problem 34
After a \(30 \%\) reduction, you purchase a dictionary for \(\$ 30.80\) What was the dictionary's price before the reduction?
View solution