How many solutions does the equation |x + 6| − 4 = c have if c = 5? If c = −10? Complete the explanation

Answer:For c = 5 → two solutionsFor c = -10 → no solutionsStep-by-step explanation:We know[tex]|a|\geq0[/tex]for any real value of a.|a| = b > 0 -  two solutions: a = b or a = -b|a| = 0 - one solution: a = 0|a| = b < 0 - no solution|x + 6| - 4 = cfor c = 5:|x + 6| - 4 = 5           add 4 to both sides|x + 6| = 9 > 0   TWO SOLUTIONSfor c = -10|x + 6| - 4 = -10           add 4 to both sides|x + 6| = -6 < 0   NO SOLUTIONSCalculate the solutions for c = 5:|x + 6| = 9 ⇔ x + 6 = 9 or x + 6 = -9         subtract 6 from both sidesx = 3 or x = -15