Sentence examples for both are solutions from inspiring English sources

Suppose both are solutions to (2.10).

Suppose and both are solutions to (3.4); then (3.5).

Suppose that x ∗ ∈ Ω and x ˜ ∈ Ω both are solutions to (3.2).

Suppose that (tilde{x}in{ varOmega }) and (hat{x}in{ varOmega }) both are solutions to the VIP (3.2).

Suppose that and both are solutions to (2.2); then and Adding up the two inequalities, we see that (2.3).

Suppose that x ∗ ∈ Γ and w ∈ Γ both are solutions to the variational inequality (3.2); then 〈 F x ∗, x ∗ − w 〉 ≤ 0, 〈 F w, w − x ∗ 〉 ≤ 0. (3.13).

Indeed, assume that both and are solutions to (3.1).

Suppose both and are solutions to (3.2), then (3.3).

Assume that both and are solutions of BVP (4.1).

Although often polarized in debates, both are realistic solutions, depending on the local circumstances.

Both are positive solutions of BVP (1.1) and satisfy (4.11).