Consider the following inequality:2(−3x+2)≤−2x−42(−3𝑥+2)≤−2𝑥−4Step 2 of 2 : Graph the solution to the given inequality.AnswerHow to enter your answer (opens in new window)KeypadKeyboard ShortcutsPrevious Part AnswerPressing the buttons will create an interval with the indicated endpoint type. The interval is graphed by moving the endpoints to the desired values. To remove graphed intervals, use the Clear button. To indicate infinity or negative infinity, drag an open end point to the end of the number line.
Question
Consider the following inequality:2(−3x+2)≤−2x−42(−3𝑥+2)≤−2𝑥−4Step 2 of 2 : Graph the solution to the given inequality.AnswerHow to enter your answer (opens in new window)KeypadKeyboard ShortcutsPrevious Part AnswerPressing the buttons will create an interval with the indicated endpoint type. The interval is graphed by moving the endpoints to the desired values. To remove graphed intervals, use the Clear button. To indicate infinity or negative infinity, drag an open end point to the end of the number line.
Solution
First, let's simplify the inequality:
2(-3x + 2) ≤ -2x - 4
Distribute the 2 on the left side:
-6x + 4 ≤ -2x - 4
Next, let's isolate x by adding 6x to both sides:
4 ≤ 4x - 4
Then, add 4 to both sides:
8 ≤ 4x
Finally, divide both sides by 4:
2 ≤ x
So, the solution to the inequality is x ≥ 2.
To graph this, you would draw a number line, put a closed circle at 2 (because the inequality includes 2), and shade everything to the right of 2 (because x is greater than or equal to 2).
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