Solve the inequality. Expression solution set using interval notation and graph the solution set using a number line. -15x+3<_-3(4x-7)
Thats supposed to be a greater than or equal to sign lol
Okee
To solve the inequality -15x + 3 ≥ -3(4x - 7), we will simplify the expressions on both sides of the inequality sign and isolate the variable x.
First, distribute -3 to the terms inside the parentheses:
-15x + 3 ≥ -12x + 21
Next, combine like terms by moving all terms involving x to one side of the inequality:
-15x + 12x ≥ 21 - 3
Simplifying further:
-3x ≥ 18
To isolate x, divide both sides of the inequality by -3. However, because we are dividing by a negative number, the inequality sign will reverse:
x ≤ 18 ÷ -3
Simplifying the division:
x ≤ -6
The solution to the inequality is x ≤ -6.
To express the solution set using interval notation, we use a square bracket [ ] to indicate that the endpoint of the interval is included in the solution. Since x can be equal to -6, we write the interval as:
[-∞, -6]
To graph the solution set on a number line, plot a closed dot at -6 (since it is included in the solution) and shade the line to the left indefinitely, as all values less than or equal to -6 satisfy the inequality.