Question

solve the linear inequality for c and graph the answer in the number line. then write the solution in inequality notation.
$-5 \geq c - 4$
show your work here
hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\
number line with -15, -10, -5, 0, 5, 10, 15, a toggle point at 0 and a toggle line to the right
solution:

Explanation:

Step1: Add 4 to both sides

To isolate \( c \), we add 4 to both sides of the inequality \(-5 \geq c - 4\). This gives us \(-5 + 4 \geq c - 4 + 4\).

Step2: Simplify both sides

Simplifying the left side: \(-5 + 4 = -1\). Simplifying the right side: \(c - 4 + 4 = c\). So the inequality becomes \(-1 \geq c\), or equivalently \(c \leq -1\).

Answer:

The solution to the inequality \(-5 \geq c - 4\) is \(c \leq -1\). To graph this on the number line, we would have a closed dot at \(-1\) (since the inequality is "less than or equal to") and an arrow pointing to the left (towards negative infinity) to represent all numbers less than or equal to \(-1\).