Solve the inequality, Graph the so integers. \[ 4 c+17 \geq 7(c+2)-3 c \]

Solve the inequality by following steps: - step0: Solve for \(c\): \(4c+17\geq 7\left(c+2\right)-3c\) - step1: Move the expression to the left side: \(4c+17-\left(7\left(c+2\right)-3c\right)\geq 0\) - step2: Calculate: \(3\geq 0\) - step3: The statement is true: \(c \in \mathbb{R}\) To solve the inequality \[ 4c + 17 \geq 7(c + 2) - 3c, \] let's simplify it step by step. 1. **Distribute on the right side:** \[ 7(c + 2) = 7c + 14. \] So the inequality becomes: \[ 4c + 17 \geq 7c + 14 - 3c. \] 2. **Combine like terms on the right side:** \[ 7c - 3c = 4c, \] thus the inequality simplifies to: \[ 4c + 17 \geq 4c + 14. \] 3. **Subtract \(4c\) from both sides:** \[ 17 \geq 14. \] This statement is always true. Since the inequality holds for all values of \(c\), the solution is: \[ c \in \mathbb{R}. \] ### Graphing the Solution The solution includes all real numbers, which means that on a number line, the entire line is shaded to indicate that every integer (and every real number) satisfies the inequality. ### Conclusion The inequality \(4c + 17 \geq 7(c + 2) - 3c\) is satisfied for all integers and real numbers.