The solution for the following system of inequalities x+5 4(x-1) ; 3-2 x>-7 on a real number line

Step-by-step solution

Given the system of inequalities: 1) x + 5 4(x - 1) 2) 3 - 2x > -7 Solving the first inequality: x + 5 4x - 4 5 + 4 4x - x 9 3x 3 x , which is x 3 . Solving the second inequality: 3 - 2x > -7 -2x > -7 - 3 -2x > -10 Dividing by -2 reverses the inequality sign: x Combining the two results, we get 3 x This corresponds to the interval [3, 5) , which is represented on the number line by a closed circle at 3 and an open circle at 5 , with the region between them shaded. This matches the fourth image. Answer: