Question

solve the inequality and graph the solution set on a number line. 5x - 4 > -x + 14

Explanation:

Step1: Add \(x\) to both sides

To isolate the \(x\) terms, we add \(x\) to both sides of the inequality \(5x - 4 > -x + 14\). This gives us \(5x + x - 4 > -x + x + 14\), which simplifies to \(6x - 4 > 14\).

Step2: Add 4 to both sides

Next, we add 4 to both sides to isolate the term with \(x\). So, \(6x - 4 + 4 > 14 + 4\), which simplifies to \(6x > 18\).

Step3: Divide by 6

Now, we divide both sides by 6 to solve for \(x\). \(\frac{6x}{6} > \frac{18}{6}\), which gives \(x > 3\).

To graph the solution set on a number line:

• Draw a number line.
• Locate the point 3. Since the inequality is \(x > 3\) (not \(x \geq 3\)), we use an open circle at 3 to indicate that 3 is not included in the solution set.
• Then, draw an arrow to the right of 3 to show that all numbers greater than 3 are part of the solution.

Answer:

The solution to the inequality \(5x - 4 > -x + 14\) is \(x > 3\). The graph has an open circle at 3 and an arrow pointing to the right.