Solve the inequality and graph the solution. (on a line plot, not a graph)

Question

–
4(b+7)–3≥1

Answer 1

To solve the inequality \(-4(b + 7) - 3 \geq 1\), we will first simplify and isolate \(b\).

1. Distribute the \(-4\): \[ -4b - 28 - 3 \geq 1 \]

2. Combine like terms: \[ -4b - 31 \geq 1 \]

3. Add \(31\) to both sides: \[ -4b \geq 1 + 31 \] \[ -4b \geq 32 \]

4. Divide by \(-4\), remembering that dividing by a negative number reverses the inequality: \[ b \leq -8 \]

The solution to the inequality is: \[ b \leq -8 \]

Graphing the Solution on a Number Line:

To represent this solution on a line plot, you would draw a number line and:

• Shade the portion of the line to the left of -8, indicating all numbers less than or equal to -8.
• Use a closed circle (or filled dot) at -8 to indicate that -8 is included in the solution set.

Here's how it will look:

<----|----|----|----|----|----|----|----|----|---->
    -10   -9   -8   -7   -6   -5   -4   -3   -2   
          ●==================================

The "●" represents the closed circle at -8 and the shaded area to the left indicates all numbers less than -8.