−2(3z−4)≤−2z+28−2(3𝑧−4)≤−2𝑧+28Step 2 of 2 : Graph the solution to the given inequality.AnswerHow to enter your answer (opens in new window)KeypadKeyboard ShortcutsPrevious Part Answer:Pressing 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
−2(3z−4)≤−2z+28−2(3𝑧−4)≤−2𝑧+28Step 2 of 2 : Graph the solution to the given inequality.AnswerHow to enter your answer (opens in new window)KeypadKeyboard ShortcutsPrevious Part Answer:Pressing 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(3z - 4) ≤ -2z + 28
Distribute the -2 on the left side:
-6z + 8 ≤ -2z + 28
Next, let's get all the z terms on one side and the constants on the other. Add 6z to both sides:
8 ≤ 4z + 28
Then, subtract 28 from both sides:
-20 ≤ 4z
Finally, divide by 4:
-5 ≤ z
So, the solution to the inequality is z ≥ -5.
To graph this, you would draw a number line, put a closed circle at -5 (because -5 is included in the solution), and shade everything to the right of -5.
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