Solve and graph the solution for this inequality. −3x+5≤23. And explain the steps.
To solve the inequality −3x + 5 ≤ 23, we want to isolate the variable x.
First, we subtract 5 from both sides of the inequality:
-3x + 5 - 5 ≤ 23 - 5
-3x ≤ 18
Next, we divide both sides of the inequality by -3. Since we're dividing by a negative number, we also need to reverse the inequality sign.
-3x/(-3) ≥ 18/(-3)
x ≥ -6
The solution to the inequality is x ≥ -6. This means that any value of x that is greater than or equal to -6 satisfies the inequality.
To graph this solution on a number line, we start by marking -6 with a closed circle to indicate that -6 is included in the solution. Then, we draw a line to the right to represent all values of x greater than -6. Since the inequality is x ≥ -6, the line is shaded in the direction of larger values.
in four steps.
Apologies for the earlier confusion. Here is a step-by-step solution in four steps:
Step 1: Subtract 5 from both sides of the inequality:
-3x + 5 - 5 ≤ 23 - 5
-3x ≤ 18
Step 2: Divide both sides of the inequality by -3. Since we are dividing by a negative number, the inequality sign needs to be reversed:
-3x / (-3) ≥ 18 / (-3)
x ≥ -6
Step 3: The solution to the inequality is x ≥ -6. This means that any value of x that is greater than or equal to -6 satisfies the inequality.
Step 4: To graph this solution on a number line, start by placing a closed circle on -6 to indicate that it is included in the solution. Then, draw a line to the right to represent all values of x greater than -6. Since the inequality is x ≥ -6, the line is shaded in the direction of larger values.