Solve the inequality and graph the solution real number line.
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Question

Quizplus · Accepted Answer

To solve the inequality, we first simplify the expression inside the absolute value: |x - 1| - 3 ≥ -7 Add 3 to both sides: |x - 1| ≥ -4 Since the absolute value of any number is always non-negative, we can see that the inequality is true for all real numbers. Therefore, the solution is the entire real number line, which we can graph as: <-------(-∞)--------------(∞)-------> First, we can simplify the inequality by multiplying both sides by 2: $$2x + 3 > 7x - 5$$ Simplifying further, we can subtract 2x from both sides: $$3 > 5x - 5$$ Next, we add 5 to both sides: $$8 > 5x$$ Finally, we divide both sides by 5: $$\frac{8}{5} > x$$ Or, in interval notation: $$x < \frac{8}{5}$$ To graph the solution on the number line, we plot an open circle at $x=\frac{8}{5}$ (since the inequality is strict), and shade to the left of it to indicate all the values of x that satisfy the inequality. This gives us choice B as the correct graph.

Solve the Inequality and Graph the Solution Real Number Line