Question

question
solve for x and graph the solution on the number line below.
58 ≥ 5x + 3 > -42
answer attempt 1 out of 2
inequality notation:
number line:
click and drag to plot line.

Explanation:

Step1: Solve the left inequality

We have the compound inequality \(58\geq5x + 3>-42\). First, solve the left - hand side of the compound inequality \(58\geq5x + 3\).
Subtract 3 from both sides: \(58 - 3\geq5x+3 - 3\), which simplifies to \(55\geq5x\).
Divide both sides by 5: \(\frac{55}{5}\geq\frac{5x}{5}\), so \(11\geq x\) or \(x\leq11\).

Step2: Solve the right inequality

Now, solve the right - hand side of the compound inequality \(5x + 3>-42\).
Subtract 3 from both sides: \(5x+3 - 3>-42 - 3\), which simplifies to \(5x>-45\).
Divide both sides by 5: \(\frac{5x}{5}>\frac{-45}{5}\), so \(x > - 9\).

Step3: Combine the solutions

Combining the two solutions \(x\leq11\) and \(x > - 9\), we get the compound inequality \(-9 < x\leq11\).

For the number line graph:

• We use an open circle at \(x=-9\) (because \(x > - 9\), the inequality is strict) and a closed circle at \(x = 11\) (because \(x\leq11\), the inequality is non - strict).
• Then we draw a line segment connecting the two points, with the open circle at \(-9\) and the closed circle at \(11\), and the line is shaded between \(-9\) and \(11\) (including \(11\) and excluding \(-9\)).

Answer:

Inequality Notation: \(-9 < x\leq11\)
For the number line: Open circle at \(-9\), closed circle at \(11\), and shade the region between \(-9\) and \(11\).