Solve Each Inequality. Graph the solution. Show your Work.
2(5−3x)<x−4(3−x)
Let's solve the inequality step by step.
2(5 - 3x) < x - 4(3 - x)
First, distribute the 2 to the terms inside the parentheses:
10 - 6x < x - 12 + 4x
Combine like terms:
-6x + 10 < 5x - 12
Next, add 6x to both sides to isolate the x term:
10 < 11x - 12
Add 12 to both sides:
22 < 11x
Finally, divide both sides by 11 to solve for x:
2 < x
Now let's graph the solution on a number line. Since the inequality is "less than," we use an open circle at 2 to represent that the value is not included in the solution. Then, we draw an arrow to the right to represent all values greater than 2.
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