Solve the linear inequality. Other than empty set ∅, graph the solution set on a number line.
8x - 9 ≤ 3x - 11
Answer (2)
The solution to the inequality 8 x − 9 ≤ 3 x − 11 is x ≤ − 5 2 . This means that any number less than or equal to − 5 2 satisfies the inequality. The graph of the solution will have a solid dot at − 5 2 and shade to the left on a number line.
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To solve the linear inequality 8 x − 9 ≤ 3 x − 11 , we will follow these steps:
Isolate the variable x :
Start by getting all terms involving x on one side of the inequality. We can do this by subtracting 3 x from both sides.
8 x − 9 − 3 x ≤ 3 x − 11 − 3 x
Simplify the terms:
5 x − 9 ≤ − 11
Eliminate the constant term on the x -side:
Add 9 to both sides to move the constant term:
5 x − 9 + 9 ≤ − 11 + 9
Simplify:
5 x ≤ − 2
Solve for x :
Divide both sides by 5 to solve for x :
x ≤ 5 − 2
The solution to the inequality is x ≤ − 5 2 .
Graphing the solution set on a number line:
To graph this on a number line, draw a line and place a point at − 5 2 .
Since the inequality is "less than or equal to," use a closed or filled-in circle to indicate that − 5 2 is included in the solution set.
Shade the number line to the left of − 5 2 to indicate all numbers less than − 5 2 are included in the solution set.
The number line will look like this:
---(... )<--- with a closed circle at − 5 2 and shading to the left. This represents all x values that satisfy the inequality.
