Long exact sequence of a pair

Exercise 3.1.4 (Long exact sequence of a pair). Let \(i\colon A \to X\) be a map of animae, and let \(j\colon X_+ \to X/A\) denote the cofiber map. Show that every homology theory gives rise to a natural long exact sequence \[ \cdots \to E_n(A) \xrightarrow {i_*} E_n(X) \xrightarrow {j_*} E_n(X,A) \xrightarrow {\partial } E_{n-1}(A) \xrightarrow {i_*} E_{n-1}(X) \to \cdots . \] Formulate and prove the analogous long exact sequence for cohomology: \[ \cdots \to E^n(X,A) \xrightarrow {j^*} E^n(X) \xrightarrow {i^*} E^n(A) \xrightarrow {\partial } E^{n+1}(X,A) \xrightarrow {j^*} E^{n+1}(X) \to \cdots . \]